library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(gtsummary)
library(emulator)
## Loading required package: mvtnorm
test_df=read_csv('Project_1_data.csv') %>% janitor::clean_names()
## Rows: 948 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (10): Gender, EthnicGroup, ParentEduc, LunchType, TestPrep, ParentMarita...
## dbl (4): NrSiblings, MathScore, ReadingScore, WritingScore
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
test_df=test_df %>%
mutate(is_first_child=case_when(
is.na(is_first_child) &nr_siblings==0 ~ 'yes',
TRUE ~is_first_child
)) %>%
mutate(gender=as.factor(gender),
ethnic_group=as.factor(ethnic_group),
parent_educ=as.factor(parent_educ),
lunch_type=as.factor(lunch_type),
test_prep=as.factor(test_prep),
parent_marital_status=as.factor(parent_marital_status),
practice_sport=as.factor(practice_sport),
is_first_child=as.factor(is_first_child),
transport_means=as.factor(transport_means),
wkly_study_hours=as.factor(wkly_study_hours)) %>% drop_na()
summary(test_df)
## gender ethnic_group parent_educ lunch_type
## female:315 group A: 50 associate's degree:129 free/reduced:207
## male :275 group B:123 bachelor's degree : 71 standard :383
## group C:175 high school :123
## group D:156 master's degree : 39
## group E: 86 some college :116
## some high school :112
## test_prep parent_marital_status practice_sport is_first_child
## completed:210 divorced: 93 never : 69 no :192
## none :380 married :344 regularly:219 yes:398
## single :138 sometimes:302
## widowed : 15
##
##
## nr_siblings transport_means wkly_study_hours math_score
## Min. :0.000 private :229 < 5 :156 Min. : 0.00
## 1st Qu.:1.000 school_bus:361 > 10 :104 1st Qu.: 56.25
## Median :2.000 10-May:330 Median : 67.00
## Mean :2.129 Mean : 66.74
## 3rd Qu.:3.000 3rd Qu.: 78.00
## Max. :7.000 Max. :100.00
## reading_score writing_score
## Min. : 17.00 Min. : 10.00
## 1st Qu.: 60.00 1st Qu.: 58.00
## Median : 70.00 Median : 69.00
## Mean : 69.87 Mean : 68.92
## 3rd Qu.: 81.00 3rd Qu.: 79.00
## Max. :100.00 Max. :100.00
test_df %>%
ggplot(aes(x=math_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
test_df %>%
ggplot(aes(x=reading_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
test_df %>%
ggplot(aes(x=writing_score))+geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
stu_data=table(test_df$gender,test_df$ethnic_group)
chisq.test(stu_data)
##
## Pearson's Chi-squared test
##
## data: stu_data
## X-squared = 7.211, df = 4, p-value = 0.1251
# Loop through pairs of columns and run the chi-square test
for (i in 1:(11 - 1)) {
for (j in (i + 1):11) {
# Get the two columns to test
col1 <- test_df[[i]]
col2 <- test_df[[j]]
contingency_table <- table(col1, col2)
# Perform the chi-square test
chi_test <- chisq.test(contingency_table)
#PRint the results
if(chi_test$p.value<.05){
cat("Chi-square test for columns", colnames(test_df)[i], "and", colnames(test_df)[j], "\n")
print(chi_test)
}
}
}
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Chi-square test for columns gender and nr_siblings
##
## Pearson's Chi-squared test
##
## data: contingency_table
## X-squared = 15.086, df = 7, p-value = 0.03491
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Chi-square test for columns is_first_child and nr_siblings
##
## Pearson's Chi-squared test
##
## data: contingency_table
## X-squared = 45.266, df = 7, p-value = 1.214e-07
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
ggplot(test_df, aes(x = nr_siblings, fill = gender)) +
geom_bar(position = "fill") +
labs(y = "Proportion", title = "Pairwise Relationship")
ggplot(test_df, aes(x = nr_siblings, fill = is_first_child)) +
geom_bar(position = "fill") +
labs(y = "Proportion", title = "Pairwise Relationship")
Writing Score
df_4_mdl_write=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,writing_score)
full_fit_write=lm(writing_score ~ .^2,data=df_4_mdl_write)
summary(full_fit_write)
##
## Call:
## lm(formula = writing_score ~ .^2, data = df_4_mdl_write)
##
## Residuals:
## Min 1Q Median 3Q Max
## -36.097 -6.757 0.000 7.512 25.909
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 77.5056 16.5568
## gendermale -11.5459 8.4352
## ethnic_groupgroup B -14.6713 14.2358
## ethnic_groupgroup C -23.6506 13.4300
## ethnic_groupgroup D -6.5467 14.6194
## ethnic_groupgroup E -0.6452 13.7011
## parent_educbachelor's degree 32.2994 14.9679
## parent_educhigh school 8.9108 12.3906
## parent_educmaster's degree -13.3428 20.4548
## parent_educsome college -9.2192 12.1578
## parent_educsome high school 0.3856 11.7932
## lunch_typestandard 3.1104 8.3745
## test_prepnone -18.8143 8.7378
## parent_marital_statusmarried 16.0430 11.1254
## parent_marital_statussingle 10.7223 13.3899
## parent_marital_statuswidowed 43.4838 39.5573
## practice_sportregularly -23.0508 13.3196
## practice_sportsometimes -19.7741 13.2523
## is_first_childyes 14.2090 9.5945
## transport_meansschool_bus -3.2352 8.4932
## wkly_study_hours> 10 -19.5441 13.0836
## wkly_study_hours10-May 1.6614 10.5143
## gendermale:ethnic_groupgroup B 4.3932 5.3431
## gendermale:ethnic_groupgroup C 9.3149 5.1384
## gendermale:ethnic_groupgroup D 5.8109 5.1043
## gendermale:ethnic_groupgroup E 5.3001 5.6595
## gendermale:parent_educbachelor's degree -3.1793 4.4945
## gendermale:parent_educhigh school 1.0620 3.6653
## gendermale:parent_educmaster's degree 9.9155 6.2928
## gendermale:parent_educsome college -4.1300 3.8491
## gendermale:parent_educsome high school 0.2529 3.7808
## gendermale:lunch_typestandard -1.2039 2.6255
## gendermale:test_prepnone -0.2240 2.6166
## gendermale:parent_marital_statusmarried -0.4821 3.7301
## gendermale:parent_marital_statussingle -0.1518 4.2288
## gendermale:parent_marital_statuswidowed 1.2933 18.3113
## gendermale:practice_sportregularly -3.0622 4.4464
## gendermale:practice_sportsometimes -3.2602 4.4697
## gendermale:is_first_childyes 3.0435 2.7466
## gendermale:transport_meansschool_bus -0.1546 2.5389
## gendermale:wkly_study_hours> 10 -3.8677 3.9831
## gendermale:wkly_study_hours10-May -2.6013 3.0208
## ethnic_groupgroup B:parent_educbachelor's degree -8.3345 12.4645
## ethnic_groupgroup C:parent_educbachelor's degree -8.4712 12.4445
## ethnic_groupgroup D:parent_educbachelor's degree -9.6856 12.3505
## ethnic_groupgroup E:parent_educbachelor's degree -16.9547 14.0557
## ethnic_groupgroup B:parent_educhigh school -16.1825 7.8036
## ethnic_groupgroup C:parent_educhigh school -10.7952 7.5005
## ethnic_groupgroup D:parent_educhigh school -7.6467 7.6256
## ethnic_groupgroup E:parent_educhigh school -11.4328 8.4924
## ethnic_groupgroup B:parent_educmaster's degree 4.9001 14.9754
## ethnic_groupgroup C:parent_educmaster's degree -7.4679 13.9097
## ethnic_groupgroup D:parent_educmaster's degree 2.9024 14.1310
## ethnic_groupgroup E:parent_educmaster's degree 1.3629 14.8684
## ethnic_groupgroup B:parent_educsome college 3.2143 8.6301
## ethnic_groupgroup C:parent_educsome college 5.9797 8.1460
## ethnic_groupgroup D:parent_educsome college 9.5674 8.4844
## ethnic_groupgroup E:parent_educsome college 2.6023 8.5774
## ethnic_groupgroup B:parent_educsome high school -17.7650 8.2716
## ethnic_groupgroup C:parent_educsome high school -10.3880 7.7610
## ethnic_groupgroup D:parent_educsome high school -6.6709 7.8120
## ethnic_groupgroup E:parent_educsome high school -4.3383 8.3877
## ethnic_groupgroup B:lunch_typestandard 3.1284 5.5561
## ethnic_groupgroup C:lunch_typestandard 6.9223 5.3886
## ethnic_groupgroup D:lunch_typestandard 3.8322 5.3042
## ethnic_groupgroup E:lunch_typestandard -0.1953 6.1469
## ethnic_groupgroup B:test_prepnone 2.4242 5.6685
## ethnic_groupgroup C:test_prepnone 6.4991 5.3175
## ethnic_groupgroup D:test_prepnone 4.2882 5.3281
## ethnic_groupgroup E:test_prepnone 10.4184 5.7998
## ethnic_groupgroup B:parent_marital_statusmarried 4.0514 7.6528
## ethnic_groupgroup C:parent_marital_statusmarried -0.2301 7.0469
## ethnic_groupgroup D:parent_marital_statusmarried -10.9053 6.9504
## ethnic_groupgroup E:parent_marital_statusmarried -4.3960 7.6897
## ethnic_groupgroup B:parent_marital_statussingle 10.5415 9.0607
## ethnic_groupgroup C:parent_marital_statussingle 2.1275 8.5665
## ethnic_groupgroup D:parent_marital_statussingle -2.6676 8.2778
## ethnic_groupgroup E:parent_marital_statussingle 3.1117 9.5410
## ethnic_groupgroup B:parent_marital_statuswidowed 73.8433 101.3778
## ethnic_groupgroup C:parent_marital_statuswidowed 114.3340 82.3923
## ethnic_groupgroup D:parent_marital_statuswidowed 12.1039 83.0580
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 14.5020 10.1514
## ethnic_groupgroup C:practice_sportregularly 15.9609 10.0599
## ethnic_groupgroup D:practice_sportregularly 11.8248 11.2295
## ethnic_groupgroup E:practice_sportregularly 12.9574 10.2802
## ethnic_groupgroup B:practice_sportsometimes 12.6309 10.8289
## ethnic_groupgroup C:practice_sportsometimes 22.0758 10.5328
## ethnic_groupgroup D:practice_sportsometimes 12.1147 11.6115
## ethnic_groupgroup E:practice_sportsometimes 12.5339 10.5863
## ethnic_groupgroup B:is_first_childyes 9.7409 5.6253
## ethnic_groupgroup C:is_first_childyes 3.4474 5.3065
## ethnic_groupgroup D:is_first_childyes 1.8617 5.3681
## ethnic_groupgroup E:is_first_childyes 2.7052 6.0462
## ethnic_groupgroup B:transport_meansschool_bus -7.4751 5.6284
## ethnic_groupgroup C:transport_meansschool_bus -11.2746 5.1972
## ethnic_groupgroup D:transport_meansschool_bus -5.1875 5.1920
## ethnic_groupgroup E:transport_meansschool_bus -12.0724 6.1289
## ethnic_groupgroup B:wkly_study_hours> 10 -5.9602 9.5818
## ethnic_groupgroup C:wkly_study_hours> 10 1.9360 9.4624
## ethnic_groupgroup D:wkly_study_hours> 10 6.7581 9.4492
## ethnic_groupgroup E:wkly_study_hours> 10 0.4986 10.2937
## ethnic_groupgroup B:wkly_study_hours10-May -5.8066 8.0474
## ethnic_groupgroup C:wkly_study_hours10-May 1.8457 7.8744
## ethnic_groupgroup D:wkly_study_hours10-May 2.9555 8.0075
## ethnic_groupgroup E:wkly_study_hours10-May -1.4251 8.6215
## parent_educbachelor's degree:lunch_typestandard 0.9925 4.8362
## parent_educhigh school:lunch_typestandard 0.9740 3.9027
## parent_educmaster's degree:lunch_typestandard 6.9772 7.1530
## parent_educsome college:lunch_typestandard 5.3543 3.9343
## parent_educsome high school:lunch_typestandard 5.7895 4.0754
## parent_educbachelor's degree:test_prepnone -1.3131 4.4623
## parent_educhigh school:test_prepnone 1.8447 4.2737
## parent_educmaster's degree:test_prepnone -2.3089 7.6077
## parent_educsome college:test_prepnone -1.8819 4.0056
## parent_educsome high school:test_prepnone 2.4708 3.8740
## parent_educbachelor's degree:parent_marital_statusmarried -17.2754 7.9642
## parent_educhigh school:parent_marital_statusmarried 2.5731 5.6012
## parent_educmaster's degree:parent_marital_statusmarried 4.5317 8.1036
## parent_educsome college:parent_marital_statusmarried -4.8368 5.5157
## parent_educsome high school:parent_marital_statusmarried -3.8229 5.4356
## parent_educbachelor's degree:parent_marital_statussingle -16.6290 8.5852
## parent_educhigh school:parent_marital_statussingle 6.4988 6.1186
## parent_educmaster's degree:parent_marital_statussingle 1.5045 8.6504
## parent_educsome college:parent_marital_statussingle -4.6580 6.1430
## parent_educsome high school:parent_marital_statussingle -3.7573 6.0684
## parent_educbachelor's degree:parent_marital_statuswidowed -20.6113 84.4043
## parent_educhigh school:parent_marital_statuswidowed -74.8517 92.8678
## parent_educmaster's degree:parent_marital_statuswidowed -98.2733 48.6482
## parent_educsome college:parent_marital_statuswidowed -87.5058 60.9959
## parent_educsome high school:parent_marital_statuswidowed -61.8441 73.1065
## parent_educbachelor's degree:practice_sportregularly 1.8608 8.2226
## parent_educhigh school:practice_sportregularly -10.9775 7.0762
## parent_educmaster's degree:practice_sportregularly 1.5289 9.9993
## parent_educsome college:practice_sportregularly -0.1518 7.1960
## parent_educsome high school:practice_sportregularly -3.2753 6.9492
## parent_educbachelor's degree:practice_sportsometimes -8.3616 7.8902
## parent_educhigh school:practice_sportsometimes -10.1532 6.7020
## parent_educmaster's degree:practice_sportsometimes 6.4978 8.3297
## parent_educsome college:practice_sportsometimes 2.7525 6.9253
## parent_educsome high school:practice_sportsometimes -1.5359 6.5116
## parent_educbachelor's degree:is_first_childyes 5.9213 4.8829
## parent_educhigh school:is_first_childyes 8.2978 4.1681
## parent_educmaster's degree:is_first_childyes 4.0575 7.2904
## parent_educsome college:is_first_childyes 11.3686 4.0703
## parent_educsome high school:is_first_childyes 6.6910 4.0992
## parent_educbachelor's degree:transport_meansschool_bus 2.9865 4.8745
## parent_educhigh school:transport_meansschool_bus 4.2359 3.8916
## parent_educmaster's degree:transport_meansschool_bus 7.9641 6.0004
## parent_educsome college:transport_meansschool_bus 2.9693 3.9628
## parent_educsome high school:transport_meansschool_bus 6.6974 4.0323
## parent_educbachelor's degree:wkly_study_hours> 10 -10.0969 7.1918
## parent_educhigh school:wkly_study_hours> 10 -8.9401 5.9867
## parent_educmaster's degree:wkly_study_hours> 10 -0.4929 12.9542
## parent_educsome college:wkly_study_hours> 10 -7.9346 6.0260
## parent_educsome high school:wkly_study_hours> 10 -9.2345 6.1375
## parent_educbachelor's degree:wkly_study_hours10-May -3.0831 4.9986
## parent_educhigh school:wkly_study_hours10-May -11.4380 4.6604
## parent_educmaster's degree:wkly_study_hours10-May -2.4586 6.6645
## parent_educsome college:wkly_study_hours10-May -4.9978 4.7455
## parent_educsome high school:wkly_study_hours10-May -9.0404 5.0069
## lunch_typestandard:test_prepnone -2.5751 2.9272
## lunch_typestandard:parent_marital_statusmarried -7.6602 3.8303
## lunch_typestandard:parent_marital_statussingle -4.8424 4.4351
## lunch_typestandard:parent_marital_statuswidowed -0.3401 75.8094
## lunch_typestandard:practice_sportregularly 9.3167 5.0489
## lunch_typestandard:practice_sportsometimes 11.9692 4.8670
## lunch_typestandard:is_first_childyes -3.2287 2.9659
## lunch_typestandard:transport_meansschool_bus -2.5877 2.7218
## lunch_typestandard:wkly_study_hours> 10 6.6183 4.1533
## lunch_typestandard:wkly_study_hours10-May 0.2394 3.1068
## test_prepnone:parent_marital_statusmarried 1.3790 3.8961
## test_prepnone:parent_marital_statussingle -2.2649 4.4856
## test_prepnone:parent_marital_statuswidowed -56.1241 39.6071
## test_prepnone:practice_sportregularly 2.1756 4.8701
## test_prepnone:practice_sportsometimes 4.8914 4.7728
## test_prepnone:is_first_childyes -0.6209 2.9395
## test_prepnone:transport_meansschool_bus 2.2476 2.6727
## test_prepnone:wkly_study_hours> 10 -2.8715 4.1954
## test_prepnone:wkly_study_hours10-May 2.5604 3.3110
## parent_marital_statusmarried:practice_sportregularly 4.6749 6.2606
## parent_marital_statussingle:practice_sportregularly -3.7080 8.1872
## parent_marital_statuswidowed:practice_sportregularly -2.7432 80.1680
## parent_marital_statusmarried:practice_sportsometimes 2.9212 6.1741
## parent_marital_statussingle:practice_sportsometimes -4.2724 8.0039
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -15.6491 4.6054
## parent_marital_statussingle:is_first_childyes -7.5649 5.1042
## parent_marital_statuswidowed:is_first_childyes 39.8253 28.4103
## parent_marital_statusmarried:transport_meansschool_bus 4.5994 3.8033
## parent_marital_statussingle:transport_meansschool_bus 0.4248 4.3343
## parent_marital_statuswidowed:transport_meansschool_bus -24.3230 18.4632
## parent_marital_statusmarried:wkly_study_hours> 10 19.5443 5.9414
## parent_marital_statussingle:wkly_study_hours> 10 25.1083 6.6075
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 5.3774 4.3617
## parent_marital_statussingle:wkly_study_hours10-May 7.7403 4.8173
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -5.8879 5.6556
## practice_sportsometimes:is_first_childyes -7.2854 5.5185
## practice_sportregularly:transport_meansschool_bus 9.5708 4.7258
## practice_sportsometimes:transport_meansschool_bus 6.1714 4.5868
## practice_sportregularly:wkly_study_hours> 10 5.1152 6.7000
## practice_sportsometimes:wkly_study_hours> 10 3.1990 6.5717
## practice_sportregularly:wkly_study_hours10-May 6.9393 5.1561
## practice_sportsometimes:wkly_study_hours10-May -0.3073 5.0837
## is_first_childyes:transport_meansschool_bus -3.0863 2.8768
## is_first_childyes:wkly_study_hours> 10 3.0112 4.3247
## is_first_childyes:wkly_study_hours10-May -2.5351 3.2646
## transport_meansschool_bus:wkly_study_hours> 10 2.0199 4.1559
## transport_meansschool_bus:wkly_study_hours10-May 1.8077 3.0009
## t value Pr(>|t|)
## (Intercept) 4.681 3.96e-06 ***
## gendermale -1.369 0.171871
## ethnic_groupgroup B -1.031 0.303382
## ethnic_groupgroup C -1.761 0.079032 .
## ethnic_groupgroup D -0.448 0.654545
## ethnic_groupgroup E -0.047 0.962465
## parent_educbachelor's degree 2.158 0.031556 *
## parent_educhigh school 0.719 0.472484
## parent_educmaster's degree -0.652 0.514593
## parent_educsome college -0.758 0.448740
## parent_educsome high school 0.033 0.973933
## lunch_typestandard 0.371 0.710536
## test_prepnone -2.153 0.031925 *
## parent_marital_statusmarried 1.442 0.150115
## parent_marital_statussingle 0.801 0.423760
## parent_marital_statuswidowed 1.099 0.272344
## practice_sportregularly -1.731 0.084330 .
## practice_sportsometimes -1.492 0.136489
## is_first_childyes 1.481 0.139442
## transport_meansschool_bus -0.381 0.703477
## wkly_study_hours> 10 -1.494 0.136054
## wkly_study_hours10-May 0.158 0.874530
## gendermale:ethnic_groupgroup B 0.822 0.411462
## gendermale:ethnic_groupgroup C 1.813 0.070644 .
## gendermale:ethnic_groupgroup D 1.138 0.255657
## gendermale:ethnic_groupgroup E 0.937 0.349605
## gendermale:parent_educbachelor's degree -0.707 0.479756
## gendermale:parent_educhigh school 0.290 0.772172
## gendermale:parent_educmaster's degree 1.576 0.115922
## gendermale:parent_educsome college -1.073 0.283958
## gendermale:parent_educsome high school 0.067 0.946710
## gendermale:lunch_typestandard -0.459 0.646819
## gendermale:test_prepnone -0.086 0.931825
## gendermale:parent_marital_statusmarried -0.129 0.897232
## gendermale:parent_marital_statussingle -0.036 0.971377
## gendermale:parent_marital_statuswidowed 0.071 0.943731
## gendermale:practice_sportregularly -0.689 0.491428
## gendermale:practice_sportsometimes -0.729 0.466204
## gendermale:is_first_childyes 1.108 0.268521
## gendermale:transport_meansschool_bus -0.061 0.951464
## gendermale:wkly_study_hours> 10 -0.971 0.332150
## gendermale:wkly_study_hours10-May -0.861 0.389706
## ethnic_groupgroup B:parent_educbachelor's degree -0.669 0.504113
## ethnic_groupgroup C:parent_educbachelor's degree -0.681 0.496462
## ethnic_groupgroup D:parent_educbachelor's degree -0.784 0.433391
## ethnic_groupgroup E:parent_educbachelor's degree -1.206 0.228465
## ethnic_groupgroup B:parent_educhigh school -2.074 0.038774 *
## ethnic_groupgroup C:parent_educhigh school -1.439 0.150891
## ethnic_groupgroup D:parent_educhigh school -1.003 0.316603
## ethnic_groupgroup E:parent_educhigh school -1.346 0.179020
## ethnic_groupgroup B:parent_educmaster's degree 0.327 0.743685
## ethnic_groupgroup C:parent_educmaster's degree -0.537 0.591656
## ethnic_groupgroup D:parent_educmaster's degree 0.205 0.837375
## ethnic_groupgroup E:parent_educmaster's degree 0.092 0.927013
## ethnic_groupgroup B:parent_educsome college 0.372 0.709764
## ethnic_groupgroup C:parent_educsome college 0.734 0.463358
## ethnic_groupgroup D:parent_educsome college 1.128 0.260175
## ethnic_groupgroup E:parent_educsome college 0.303 0.761758
## ethnic_groupgroup B:parent_educsome high school -2.148 0.032364 *
## ethnic_groupgroup C:parent_educsome high school -1.338 0.181530
## ethnic_groupgroup D:parent_educsome high school -0.854 0.393676
## ethnic_groupgroup E:parent_educsome high school -0.517 0.605302
## ethnic_groupgroup B:lunch_typestandard 0.563 0.573723
## ethnic_groupgroup C:lunch_typestandard 1.285 0.199701
## ethnic_groupgroup D:lunch_typestandard 0.722 0.470435
## ethnic_groupgroup E:lunch_typestandard -0.032 0.974675
## ethnic_groupgroup B:test_prepnone 0.428 0.669136
## ethnic_groupgroup C:test_prepnone 1.222 0.222374
## ethnic_groupgroup D:test_prepnone 0.805 0.421423
## ethnic_groupgroup E:test_prepnone 1.796 0.073229 .
## ethnic_groupgroup B:parent_marital_statusmarried 0.529 0.596832
## ethnic_groupgroup C:parent_marital_statusmarried -0.033 0.973967
## ethnic_groupgroup D:parent_marital_statusmarried -1.569 0.117469
## ethnic_groupgroup E:parent_marital_statusmarried -0.572 0.567873
## ethnic_groupgroup B:parent_marital_statussingle 1.163 0.245378
## ethnic_groupgroup C:parent_marital_statussingle 0.248 0.803994
## ethnic_groupgroup D:parent_marital_statussingle -0.322 0.747428
## ethnic_groupgroup E:parent_marital_statussingle 0.326 0.744500
## ethnic_groupgroup B:parent_marital_statuswidowed 0.728 0.466816
## ethnic_groupgroup C:parent_marital_statuswidowed 1.388 0.166042
## ethnic_groupgroup D:parent_marital_statuswidowed 0.146 0.884212
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 1.429 0.153942
## ethnic_groupgroup C:practice_sportregularly 1.587 0.113432
## ethnic_groupgroup D:practice_sportregularly 1.053 0.293000
## ethnic_groupgroup E:practice_sportregularly 1.260 0.208281
## ethnic_groupgroup B:practice_sportsometimes 1.166 0.244177
## ethnic_groupgroup C:practice_sportsometimes 2.096 0.036745 *
## ethnic_groupgroup D:practice_sportsometimes 1.043 0.297450
## ethnic_groupgroup E:practice_sportsometimes 1.184 0.237159
## ethnic_groupgroup B:is_first_childyes 1.732 0.084147 .
## ethnic_groupgroup C:is_first_childyes 0.650 0.516308
## ethnic_groupgroup D:is_first_childyes 0.347 0.728926
## ethnic_groupgroup E:is_first_childyes 0.447 0.654819
## ethnic_groupgroup B:transport_meansschool_bus -1.328 0.184937
## ethnic_groupgroup C:transport_meansschool_bus -2.169 0.030669 *
## ethnic_groupgroup D:transport_meansschool_bus -0.999 0.318358
## ethnic_groupgroup E:transport_meansschool_bus -1.970 0.049590 *
## ethnic_groupgroup B:wkly_study_hours> 10 -0.622 0.534294
## ethnic_groupgroup C:wkly_study_hours> 10 0.205 0.837996
## ethnic_groupgroup D:wkly_study_hours> 10 0.715 0.474919
## ethnic_groupgroup E:wkly_study_hours> 10 0.048 0.961392
## ethnic_groupgroup B:wkly_study_hours10-May -0.722 0.471008
## ethnic_groupgroup C:wkly_study_hours10-May 0.234 0.814802
## ethnic_groupgroup D:wkly_study_hours10-May 0.369 0.712263
## ethnic_groupgroup E:wkly_study_hours10-May -0.165 0.868800
## parent_educbachelor's degree:lunch_typestandard 0.205 0.837509
## parent_educhigh school:lunch_typestandard 0.250 0.803050
## parent_educmaster's degree:lunch_typestandard 0.975 0.329964
## parent_educsome college:lunch_typestandard 1.361 0.174329
## parent_educsome high school:lunch_typestandard 1.421 0.156247
## parent_educbachelor's degree:test_prepnone -0.294 0.768711
## parent_educhigh school:test_prepnone 0.432 0.666242
## parent_educmaster's degree:test_prepnone -0.303 0.761677
## parent_educsome college:test_prepnone -0.470 0.638759
## parent_educsome high school:test_prepnone 0.638 0.523982
## parent_educbachelor's degree:parent_marital_statusmarried -2.169 0.030688 *
## parent_educhigh school:parent_marital_statusmarried 0.459 0.646215
## parent_educmaster's degree:parent_marital_statusmarried 0.559 0.576337
## parent_educsome college:parent_marital_statusmarried -0.877 0.381080
## parent_educsome high school:parent_marital_statusmarried -0.703 0.482292
## parent_educbachelor's degree:parent_marital_statussingle -1.937 0.053489 .
## parent_educhigh school:parent_marital_statussingle 1.062 0.288837
## parent_educmaster's degree:parent_marital_statussingle 0.174 0.862019
## parent_educsome college:parent_marital_statussingle -0.758 0.448762
## parent_educsome high school:parent_marital_statussingle -0.619 0.536181
## parent_educbachelor's degree:parent_marital_statuswidowed -0.244 0.807209
## parent_educhigh school:parent_marital_statuswidowed -0.806 0.420742
## parent_educmaster's degree:parent_marital_statuswidowed -2.020 0.044071 *
## parent_educsome college:parent_marital_statuswidowed -1.435 0.152213
## parent_educsome high school:parent_marital_statuswidowed -0.846 0.398112
## parent_educbachelor's degree:practice_sportregularly 0.226 0.821088
## parent_educhigh school:practice_sportregularly -1.551 0.121650
## parent_educmaster's degree:practice_sportregularly 0.153 0.878559
## parent_educsome college:practice_sportregularly -0.021 0.983182
## parent_educsome high school:practice_sportregularly -0.471 0.637680
## parent_educbachelor's degree:practice_sportsometimes -1.060 0.289930
## parent_educhigh school:practice_sportsometimes -1.515 0.130609
## parent_educmaster's degree:practice_sportsometimes 0.780 0.435832
## parent_educsome college:practice_sportsometimes 0.397 0.691259
## parent_educsome high school:practice_sportsometimes -0.236 0.813660
## parent_educbachelor's degree:is_first_childyes 1.213 0.226003
## parent_educhigh school:is_first_childyes 1.991 0.047213 *
## parent_educmaster's degree:is_first_childyes 0.557 0.578162
## parent_educsome college:is_first_childyes 2.793 0.005483 **
## parent_educsome high school:is_first_childyes 1.632 0.103442
## parent_educbachelor's degree:transport_meansschool_bus 0.613 0.540462
## parent_educhigh school:transport_meansschool_bus 1.088 0.277080
## parent_educmaster's degree:transport_meansschool_bus 1.327 0.185211
## parent_educsome college:transport_meansschool_bus 0.749 0.454133
## parent_educsome high school:transport_meansschool_bus 1.661 0.097541 .
## parent_educbachelor's degree:wkly_study_hours> 10 -1.404 0.161148
## parent_educhigh school:wkly_study_hours> 10 -1.493 0.136173
## parent_educmaster's degree:wkly_study_hours> 10 -0.038 0.969667
## parent_educsome college:wkly_study_hours> 10 -1.317 0.188716
## parent_educsome high school:wkly_study_hours> 10 -1.505 0.133251
## parent_educbachelor's degree:wkly_study_hours10-May -0.617 0.537741
## parent_educhigh school:wkly_study_hours10-May -2.454 0.014560 *
## parent_educmaster's degree:wkly_study_hours10-May -0.369 0.712402
## parent_educsome college:wkly_study_hours10-May -1.053 0.292924
## parent_educsome high school:wkly_study_hours10-May -1.806 0.071766 .
## lunch_typestandard:test_prepnone -0.880 0.379567
## lunch_typestandard:parent_marital_statusmarried -2.000 0.046216 *
## lunch_typestandard:parent_marital_statussingle -1.092 0.275596
## lunch_typestandard:parent_marital_statuswidowed -0.004 0.996423
## lunch_typestandard:practice_sportregularly 1.845 0.065767 .
## lunch_typestandard:practice_sportsometimes 2.459 0.014363 *
## lunch_typestandard:is_first_childyes -1.089 0.277020
## lunch_typestandard:transport_meansschool_bus -0.951 0.342335
## lunch_typestandard:wkly_study_hours> 10 1.593 0.111876
## lunch_typestandard:wkly_study_hours10-May 0.077 0.938623
## test_prepnone:parent_marital_statusmarried 0.354 0.723573
## test_prepnone:parent_marital_statussingle -0.505 0.613893
## test_prepnone:parent_marital_statuswidowed -1.417 0.157290
## test_prepnone:practice_sportregularly 0.447 0.655333
## test_prepnone:practice_sportsometimes 1.025 0.306088
## test_prepnone:is_first_childyes -0.211 0.832828
## test_prepnone:transport_meansschool_bus 0.841 0.400913
## test_prepnone:wkly_study_hours> 10 -0.684 0.494109
## test_prepnone:wkly_study_hours10-May 0.773 0.439827
## parent_marital_statusmarried:practice_sportregularly 0.747 0.455689
## parent_marital_statussingle:practice_sportregularly -0.453 0.650870
## parent_marital_statuswidowed:practice_sportregularly -0.034 0.972721
## parent_marital_statusmarried:practice_sportsometimes 0.473 0.636383
## parent_marital_statussingle:practice_sportsometimes -0.534 0.593797
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -3.398 0.000750 ***
## parent_marital_statussingle:is_first_childyes -1.482 0.139140
## parent_marital_statuswidowed:is_first_childyes 1.402 0.161788
## parent_marital_statusmarried:transport_meansschool_bus 1.209 0.227285
## parent_marital_statussingle:transport_meansschool_bus 0.098 0.921980
## parent_marital_statuswidowed:transport_meansschool_bus -1.317 0.188500
## parent_marital_statusmarried:wkly_study_hours> 10 3.289 0.001097 **
## parent_marital_statussingle:wkly_study_hours> 10 3.800 0.000168 ***
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 1.233 0.218380
## parent_marital_statussingle:wkly_study_hours10-May 1.607 0.108933
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -1.041 0.298498
## practice_sportsometimes:is_first_childyes -1.320 0.187560
## practice_sportregularly:transport_meansschool_bus 2.025 0.043539 *
## practice_sportsometimes:transport_meansschool_bus 1.345 0.179276
## practice_sportregularly:wkly_study_hours> 10 0.763 0.445653
## practice_sportsometimes:wkly_study_hours> 10 0.487 0.626687
## practice_sportregularly:wkly_study_hours10-May 1.346 0.179149
## practice_sportsometimes:wkly_study_hours10-May -0.060 0.951832
## is_first_childyes:transport_meansschool_bus -1.073 0.284019
## is_first_childyes:wkly_study_hours> 10 0.696 0.486682
## is_first_childyes:wkly_study_hours10-May -0.777 0.437906
## transport_meansschool_bus:wkly_study_hours> 10 0.486 0.627215
## transport_meansschool_bus:wkly_study_hours10-May 0.602 0.547281
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.42 on 383 degrees of freedom
## Multiple R-squared: 0.5844, Adjusted R-squared: 0.3608
## F-statistic: 2.614 on 206 and 383 DF, p-value: 2.56e-16
stepwise_model_write <- step(full_fit_write, direction = "both", trace = 1)
## Start: AIC=3131.41
## writing_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours)^2
##
## Df Sum of Sq RSS AIC
## - parent_educ:test_prep 5 245.4 59282 3123.9
## - ethnic_group:parent_educ 20 3361.8 62398 3124.1
## - gender:parent_marital_status 3 4.9 59041 3125.5
## - parent_educ:wkly_study_hours 10 1468.0 60504 3125.9
## - ethnic_group:wkly_study_hours 8 1092.4 60129 3126.2
## - parent_educ:transport_means 5 547.3 59583 3126.9
## - parent_marital_status:practice_sport 4 348.1 59384 3126.9
## - parent_educ:lunch_type 5 600.2 59636 3127.4
## - transport_means:wkly_study_hours 2 63.5 59100 3128.1
## - gender:practice_sport 2 85.6 59122 3128.3
## - ethnic_group:lunch_type 4 513.8 59550 3128.5
## - parent_educ:parent_marital_status 13 2409.8 61446 3129.0
## - gender:wkly_study_hours 2 167.8 59204 3129.1
## - gender:transport_means 1 0.6 59037 3129.4
## - gender:test_prep 1 1.1 59037 3129.4
## - test_prep:is_first_child 1 6.9 59043 3129.5
## - test_prep:parent_marital_status 2 211.7 59248 3129.5
## - gender:lunch_type 1 32.4 59069 3129.7
## - test_prep:practice_sport 2 244.8 59281 3129.8
## - gender:ethnic_group 4 652.4 59689 3129.9
## - gender:parent_educ 5 856.7 59893 3129.9
## - practice_sport:is_first_child 2 277.0 59313 3130.2
## - test_prep:transport_means 1 109.0 59145 3130.5
## - lunch_type:test_prep 1 119.3 59155 3130.6
## - lunch_type:transport_means 1 139.3 59176 3130.8
## - is_first_child:wkly_study_hours 2 340.9 59377 3130.8
## - ethnic_group:is_first_child 4 746.0 59782 3130.8
## - ethnic_group:test_prep 4 757.2 59793 3130.9
## - is_first_child:transport_means 1 177.4 59214 3131.2
## - lunch_type:is_first_child 1 182.7 59219 3131.2
## - ethnic_group:practice_sport 8 1610.3 60646 3131.3
## - gender:is_first_child 1 189.3 59225 3131.3
## - test_prep:wkly_study_hours 2 400.5 59437 3131.4
## <none> 59036 3131.4
## - parent_educ:practice_sport 10 2078.2 61114 3131.8
## - lunch_type:wkly_study_hours 2 509.7 59546 3132.5
## - parent_marital_status:transport_means 3 755.0 59791 3132.9
## - ethnic_group:parent_marital_status 9 1983.9 61020 3132.9
## - practice_sport:wkly_study_hours 4 995.1 60031 3133.3
## - lunch_type:parent_marital_status 2 650.3 59687 3133.9
## - practice_sport:transport_means 2 679.6 59716 3134.2
## - ethnic_group:transport_means 4 1108.7 60145 3134.4
## - parent_educ:is_first_child 5 1316.0 60352 3134.4
## - lunch_type:practice_sport 2 950.1 59986 3136.8
## - parent_marital_status:wkly_study_hours 4 2324.9 61361 3146.2
## - parent_marital_status:is_first_child 2 2312.7 61349 3150.1
##
## Step: AIC=3123.86
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_educ 20 3285.4 62567 3115.7
## - gender:parent_marital_status 3 7.5 59289 3117.9
## - ethnic_group:wkly_study_hours 8 1092.3 60374 3118.6
## - parent_marital_status:practice_sport 4 343.6 59625 3119.3
## - parent_educ:wkly_study_hours 10 1612.0 60894 3119.7
## - parent_educ:lunch_type 5 596.6 59878 3119.8
## - parent_educ:transport_means 5 601.4 59883 3119.8
## - transport_means:wkly_study_hours 2 57.6 59339 3120.4
## - gender:practice_sport 2 72.1 59354 3120.6
## - ethnic_group:lunch_type 4 535.1 59817 3121.2
## - parent_educ:parent_marital_status 13 2393.4 61675 3121.2
## - gender:wkly_study_hours 2 180.9 59462 3121.7
## - test_prep:parent_marital_status 2 184.5 59466 3121.7
## - gender:test_prep 1 0.0 59282 3121.9
## - gender:transport_means 1 1.8 59283 3121.9
## - test_prep:practice_sport 2 207.8 59489 3121.9
## - test_prep:is_first_child 1 10.7 59292 3122.0
## - gender:ethnic_group 4 627.6 59909 3122.1
## - gender:lunch_type 1 24.7 59306 3122.1
## - ethnic_group:test_prep 4 639.2 59921 3122.2
## - gender:parent_educ 5 892.7 60174 3122.7
## - test_prep:transport_means 1 98.8 59380 3122.8
## - is_first_child:wkly_study_hours 2 302.5 59584 3122.9
## - lunch_type:test_prep 1 116.0 59398 3123.0
## - practice_sport:is_first_child 2 323.8 59605 3123.1
## - lunch_type:transport_means 1 133.6 59415 3123.2
## - gender:is_first_child 1 166.6 59448 3123.5
## - ethnic_group:practice_sport 8 1607.5 60889 3123.6
## - ethnic_group:is_first_child 4 790.6 60072 3123.7
## - lunch_type:is_first_child 1 199.8 59481 3123.8
## <none> 59282 3123.9
## - is_first_child:transport_means 1 217.5 59499 3124.0
## - test_prep:wkly_study_hours 2 441.6 59723 3124.2
## - ethnic_group:parent_marital_status 9 1922.8 61204 3124.7
## - parent_educ:practice_sport 10 2157.5 61439 3124.9
## - lunch_type:wkly_study_hours 2 549.6 59831 3125.3
## - parent_marital_status:transport_means 3 758.5 60040 3125.4
## - lunch_type:parent_marital_status 2 587.8 59869 3125.7
## - practice_sport:wkly_study_hours 4 1017.6 60299 3125.9
## - ethnic_group:transport_means 4 1123.4 60405 3126.9
## - practice_sport:transport_means 2 729.9 60011 3127.1
## - parent_educ:is_first_child 5 1429.3 60711 3127.9
## - lunch_type:practice_sport 2 950.3 60232 3129.2
## + parent_educ:test_prep 5 245.4 59036 3131.4
## - parent_marital_status:wkly_study_hours 4 2425.4 61707 3139.5
## - parent_marital_status:is_first_child 2 2368.4 61650 3143.0
##
## Step: AIC=3115.68
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:wkly_study_hours 8 838.3 63405 3107.5
## - parent_educ:wkly_study_hours 10 1310.7 63878 3107.9
## - gender:parent_marital_status 3 12.5 62579 3109.8
## - parent_educ:lunch_type 5 510.3 63077 3110.5
## - parent_marital_status:practice_sport 4 360.8 62928 3111.1
## - ethnic_group:practice_sport 8 1247.6 63815 3111.3
## - parent_educ:transport_means 5 641.0 63208 3111.7
## - gender:ethnic_group 4 522.4 63089 3112.6
## - ethnic_group:test_prep 4 527.3 63094 3112.6
## - test_prep:parent_marital_status 2 142.9 62710 3113.0
## - transport_means:wkly_study_hours 2 159.6 62726 3113.2
## - gender:wkly_study_hours 2 161.7 62729 3113.2
## - gender:parent_educ 5 828.0 63395 3113.4
## - gender:practice_sport 2 190.3 62757 3113.5
## - is_first_child:wkly_study_hours 2 192.2 62759 3113.5
## - gender:transport_means 1 0.9 62568 3113.7
## - gender:test_prep 1 1.5 62568 3113.7
## - lunch_type:test_prep 1 5.1 62572 3113.7
## - gender:lunch_type 1 8.8 62576 3113.8
## - test_prep:practice_sport 2 223.8 62791 3113.8
## - parent_educ:parent_marital_status 13 2624.7 65192 3113.9
## - gender:is_first_child 1 33.5 62600 3114.0
## - ethnic_group:lunch_type 4 675.1 63242 3114.0
## - test_prep:is_first_child 1 43.5 62610 3114.1
## - practice_sport:is_first_child 2 284.8 62852 3114.4
## - lunch_type:parent_marital_status 2 286.8 62854 3114.4
## - test_prep:transport_means 1 107.4 62674 3114.7
## - parent_educ:practice_sport 10 2081.2 64648 3115.0
## - is_first_child:transport_means 1 173.0 62740 3115.3
## - lunch_type:is_first_child 1 198.5 62765 3115.6
## - parent_marital_status:transport_means 3 631.4 63198 3115.6
## <none> 62567 3115.7
## - lunch_type:transport_means 1 233.7 62801 3115.9
## - test_prep:wkly_study_hours 2 483.1 63050 3116.2
## - ethnic_group:is_first_child 4 945.3 63512 3116.5
## - practice_sport:transport_means 2 532.5 63099 3116.7
## - ethnic_group:transport_means 4 994.0 63561 3117.0
## - practice_sport:wkly_study_hours 4 1093.7 63661 3117.9
## - ethnic_group:parent_marital_status 9 2217.3 64784 3118.2
## - parent_educ:is_first_child 5 1371.0 63938 3118.5
## - lunch_type:wkly_study_hours 2 842.3 63409 3119.6
## - lunch_type:practice_sport 2 1121.1 63688 3122.2
## + ethnic_group:parent_educ 20 3285.4 59282 3123.9
## + parent_educ:test_prep 5 169.0 62398 3124.1
## - parent_marital_status:wkly_study_hours 4 1981.5 64548 3126.1
## - parent_marital_status:is_first_child 2 2099.4 64666 3131.2
##
## Step: AIC=3107.54
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 1414.74 64820 3100.6
## - gender:parent_marital_status 3 21.12 63426 3101.7
## - parent_marital_status:practice_sport 4 273.36 63679 3102.1
## - parent_educ:lunch_type 5 538.08 63943 3102.5
## - ethnic_group:practice_sport 8 1242.25 64647 3103.0
## - parent_educ:transport_means 5 629.09 64034 3103.4
## - transport_means:wkly_study_hours 2 74.29 63480 3104.2
## - gender:ethnic_group 4 521.25 63926 3104.4
## - ethnic_group:test_prep 4 528.77 63934 3104.4
## - parent_educ:parent_marital_status 13 2521.02 65926 3104.5
## - gender:wkly_study_hours 2 111.28 63517 3104.6
## - test_prep:parent_marital_status 2 160.78 63566 3105.0
## - gender:parent_educ 5 835.10 64240 3105.3
## - gender:practice_sport 2 198.93 63604 3105.4
## - is_first_child:wkly_study_hours 2 202.74 63608 3105.4
## - lunch_type:test_prep 1 0.02 63405 3105.5
## - gender:transport_means 1 1.41 63407 3105.6
## - test_prep:practice_sport 2 223.33 63629 3105.6
## - gender:lunch_type 1 9.19 63414 3105.6
## - gender:test_prep 1 10.73 63416 3105.6
## - gender:is_first_child 1 19.04 63424 3105.7
## - lunch_type:parent_marital_status 2 263.90 63669 3106.0
## - test_prep:is_first_child 1 61.13 63466 3106.1
## - test_prep:transport_means 1 83.82 63489 3106.3
## - ethnic_group:lunch_type 4 737.87 64143 3106.4
## - practice_sport:is_first_child 2 307.72 63713 3106.4
## - parent_educ:practice_sport 10 2084.34 65490 3106.6
## - is_first_child:transport_means 1 182.81 63588 3107.2
## - lunch_type:transport_means 1 190.55 63596 3107.3
## <none> 63405 3107.5
## - lunch_type:is_first_child 1 222.45 63628 3107.6
## - parent_marital_status:transport_means 3 668.96 64074 3107.7
## - ethnic_group:is_first_child 4 906.30 64312 3107.9
## - test_prep:wkly_study_hours 2 479.44 63885 3108.0
## - practice_sport:transport_means 2 522.81 63928 3108.4
## - ethnic_group:transport_means 4 1002.86 64408 3108.8
## - ethnic_group:parent_marital_status 9 2134.54 65540 3109.1
## - parent_educ:is_first_child 5 1308.56 64714 3109.6
## - practice_sport:wkly_study_hours 4 1141.24 64546 3110.1
## - lunch_type:wkly_study_hours 2 905.28 64311 3111.9
## - lunch_type:practice_sport 2 1150.67 64556 3114.2
## + ethnic_group:wkly_study_hours 8 838.30 62567 3115.7
## + parent_educ:test_prep 5 193.76 63211 3115.7
## - parent_marital_status:wkly_study_hours 4 1837.59 65243 3116.4
## + ethnic_group:parent_educ 20 3031.37 60374 3118.6
## - parent_marital_status:is_first_child 2 1979.54 65385 3121.7
##
## Step: AIC=3100.56
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 8.23 64828 3094.6
## - parent_educ:lunch_type 5 450.88 65271 3094.7
## - ethnic_group:practice_sport 8 1175.09 65995 3095.2
## - parent_marital_status:practice_sport 4 329.09 65149 3095.5
## - parent_educ:transport_means 5 709.12 65529 3097.0
## - gender:ethnic_group 4 488.42 65308 3097.0
## - ethnic_group:test_prep 4 513.16 65333 3097.2
## - transport_means:wkly_study_hours 2 111.53 64932 3097.6
## - gender:parent_educ 5 786.39 65606 3097.7
## - test_prep:parent_marital_status 2 128.82 64949 3097.7
## - is_first_child:wkly_study_hours 2 153.41 64973 3097.9
## - ethnic_group:lunch_type 4 608.64 65429 3098.1
## - gender:practice_sport 2 169.79 64990 3098.1
## - gender:transport_means 1 0.57 64821 3098.6
## - lunch_type:test_prep 1 2.61 64823 3098.6
## - gender:wkly_study_hours 2 223.32 65043 3098.6
## - practice_sport:is_first_child 2 227.73 65048 3098.6
## - gender:lunch_type 1 9.90 64830 3098.7
## - gender:test_prep 1 17.01 64837 3098.7
## - gender:is_first_child 1 29.46 64849 3098.8
## - test_prep:is_first_child 1 46.22 64866 3099.0
## - test_prep:practice_sport 2 284.13 65104 3099.1
## - lunch_type:parent_marital_status 2 297.47 65117 3099.3
## - test_prep:transport_means 1 90.44 64910 3099.4
## - parent_educ:parent_marital_status 13 2797.67 67618 3099.5
## - lunch_type:is_first_child 1 167.64 64988 3100.1
## - practice_sport:transport_means 2 388.54 65209 3100.1
## - is_first_child:transport_means 1 187.17 65007 3100.3
## <none> 64820 3100.6
## - ethnic_group:transport_means 4 890.45 65710 3100.6
## - practice_sport:wkly_study_hours 4 895.41 65715 3100.7
## - lunch_type:transport_means 1 231.07 65051 3100.7
## - parent_marital_status:transport_means 3 689.01 65509 3100.8
## - parent_educ:practice_sport 10 2285.42 67105 3101.0
## - ethnic_group:is_first_child 4 941.18 65761 3101.1
## - test_prep:wkly_study_hours 2 567.28 65387 3101.7
## - parent_educ:is_first_child 5 1260.35 66080 3101.9
## - lunch_type:wkly_study_hours 2 732.64 65553 3103.2
## - ethnic_group:parent_marital_status 9 2313.61 67134 3103.2
## - lunch_type:practice_sport 2 1122.55 65943 3106.7
## + parent_educ:wkly_study_hours 10 1414.74 63405 3107.5
## + ethnic_group:wkly_study_hours 8 942.30 63878 3107.9
## + parent_educ:test_prep 5 254.90 64565 3108.2
## - parent_marital_status:wkly_study_hours 4 2025.70 66846 3110.7
## + ethnic_group:parent_educ 20 2750.70 62069 3115.0
## - parent_marital_status:is_first_child 2 2080.59 66901 3115.2
##
## Step: AIC=3094.63
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:lunch_type 5 453.76 65282 3088.8
## - ethnic_group:practice_sport 8 1171.59 66000 3089.2
## - parent_marital_status:practice_sport 4 327.63 65156 3089.6
## - parent_educ:transport_means 5 704.99 65533 3091.0
## - gender:ethnic_group 4 484.60 65313 3091.0
## - ethnic_group:test_prep 4 518.12 65346 3091.3
## - transport_means:wkly_study_hours 2 112.25 64940 3091.7
## - test_prep:parent_marital_status 2 129.44 64958 3091.8
## - gender:parent_educ 5 802.53 65631 3091.9
## - is_first_child:wkly_study_hours 2 150.98 64979 3092.0
## - ethnic_group:lunch_type 4 611.63 65440 3092.2
## - gender:practice_sport 2 175.34 65004 3092.2
## - gender:transport_means 1 0.68 64829 3092.6
## - lunch_type:test_prep 1 2.43 64831 3092.7
## - practice_sport:is_first_child 2 227.81 65056 3092.7
## - gender:lunch_type 1 9.03 64837 3092.7
## - gender:wkly_study_hours 2 232.70 65061 3092.7
## - gender:test_prep 1 17.92 64846 3092.8
## - gender:is_first_child 1 32.58 64861 3092.9
## - test_prep:is_first_child 1 46.46 64875 3093.1
## - test_prep:practice_sport 2 295.19 65123 3093.3
## - test_prep:transport_means 1 89.71 64918 3093.4
## - lunch_type:parent_marital_status 2 325.21 65153 3093.6
## - parent_educ:parent_marital_status 13 2846.27 67674 3094.0
## - practice_sport:transport_means 2 384.18 65212 3094.1
## - lunch_type:is_first_child 1 169.80 64998 3094.2
## - is_first_child:transport_means 1 197.72 65026 3094.4
## <none> 64828 3094.6
## - ethnic_group:transport_means 4 891.25 65719 3094.7
## - lunch_type:transport_means 1 237.39 65066 3094.8
## - practice_sport:wkly_study_hours 4 914.03 65742 3094.9
## - ethnic_group:is_first_child 4 941.88 65770 3095.1
## - parent_educ:practice_sport 10 2323.35 67152 3095.4
## - test_prep:wkly_study_hours 2 565.73 65394 3095.8
## - parent_marital_status:transport_means 3 799.54 65628 3095.9
## - parent_educ:is_first_child 5 1262.58 66091 3096.0
## - lunch_type:wkly_study_hours 2 745.49 65574 3097.4
## - ethnic_group:parent_marital_status 9 2441.41 67270 3098.4
## + gender:parent_marital_status 3 8.23 64820 3100.6
## - lunch_type:practice_sport 2 1165.09 65993 3101.1
## + parent_educ:wkly_study_hours 10 1401.85 63426 3101.7
## + ethnic_group:wkly_study_hours 8 943.83 63884 3102.0
## + parent_educ:test_prep 5 256.20 64572 3102.3
## - parent_marital_status:wkly_study_hours 4 2029.22 66857 3104.8
## + ethnic_group:parent_educ 20 2749.68 62079 3109.1
## - parent_marital_status:is_first_child 2 2115.57 66944 3109.6
##
## Step: AIC=3088.75
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:practice_sport 8 1102.72 66385 3082.6
## - parent_marital_status:practice_sport 4 362.52 65644 3084.0
## - gender:ethnic_group 4 473.96 65756 3085.0
## - parent_educ:transport_means 5 705.99 65988 3085.1
## - gender:parent_educ 5 730.18 66012 3085.3
## - ethnic_group:test_prep 4 552.03 65834 3085.7
## - test_prep:parent_marital_status 2 124.91 65407 3085.9
## - transport_means:wkly_study_hours 2 125.88 65408 3085.9
## - ethnic_group:lunch_type 4 589.22 65871 3086.1
## - is_first_child:wkly_study_hours 2 147.84 65430 3086.1
## - gender:practice_sport 2 177.50 65459 3086.3
## - gender:wkly_study_hours 2 210.11 65492 3086.6
## - gender:transport_means 1 0.48 65282 3086.8
## - lunch_type:test_prep 1 3.83 65286 3086.8
## - gender:test_prep 1 15.37 65297 3086.9
## - practice_sport:is_first_child 2 240.28 65522 3086.9
## - gender:lunch_type 1 24.06 65306 3087.0
## - test_prep:is_first_child 1 34.65 65317 3087.1
## - gender:is_first_child 1 64.33 65346 3087.3
## - lunch_type:parent_marital_status 2 294.12 65576 3087.4
## - test_prep:transport_means 1 113.55 65396 3087.8
## - test_prep:practice_sport 2 351.93 65634 3087.9
## - lunch_type:is_first_child 1 140.20 65422 3088.0
## - ethnic_group:transport_means 4 848.96 66131 3088.4
## - is_first_child:transport_means 1 183.22 65465 3088.4
## <none> 65282 3088.8
## - practice_sport:transport_means 2 445.89 65728 3088.8
## - parent_educ:parent_marital_status 13 2963.47 68245 3088.9
## - lunch_type:transport_means 1 274.34 65556 3089.2
## - ethnic_group:is_first_child 4 953.00 66235 3089.3
## - practice_sport:wkly_study_hours 4 967.93 66250 3089.4
## - parent_educ:practice_sport 10 2339.85 67622 3089.5
## - parent_educ:is_first_child 5 1226.98 66509 3089.7
## - test_prep:wkly_study_hours 2 569.64 65852 3089.9
## - parent_marital_status:transport_means 3 859.31 66141 3090.5
## - lunch_type:wkly_study_hours 2 714.94 65997 3091.2
## - ethnic_group:parent_marital_status 9 2385.39 67667 3091.9
## + parent_educ:lunch_type 5 453.76 64828 3094.6
## + gender:parent_marital_status 3 11.11 65271 3094.7
## - lunch_type:practice_sport 2 1117.40 66399 3094.8
## + ethnic_group:wkly_study_hours 8 944.83 64337 3096.1
## + parent_educ:wkly_study_hours 10 1311.24 63971 3096.8
## + parent_educ:test_prep 5 207.94 65074 3096.9
## - parent_marital_status:wkly_study_hours 4 2112.97 67395 3099.5
## + ethnic_group:parent_educ 20 2782.22 62500 3103.1
## - parent_marital_status:is_first_child 2 2274.32 67556 3104.9
##
## Step: AIC=3082.63
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:ethnic_group 4 334.06 66719 3077.6
## - parent_educ:transport_means 5 602.59 66987 3078.0
## - gender:parent_educ 5 667.19 67052 3078.5
## - parent_marital_status:practice_sport 4 536.65 66921 3079.4
## - ethnic_group:test_prep 4 578.24 66963 3079.8
## - practice_sport:is_first_child 2 144.13 66529 3079.9
## - test_prep:parent_marital_status 2 152.27 66537 3080.0
## - transport_means:wkly_study_hours 2 160.57 66545 3080.1
## - is_first_child:wkly_study_hours 2 164.84 66550 3080.1
## - gender:transport_means 1 1.29 66386 3080.6
## - gender:test_prep 1 5.51 66390 3080.7
## - gender:lunch_type 1 10.61 66395 3080.7
## - ethnic_group:lunch_type 4 704.57 67089 3080.9
## - test_prep:is_first_child 1 28.20 66413 3080.9
## - gender:is_first_child 1 30.57 66415 3080.9
## - lunch_type:test_prep 1 31.63 66416 3080.9
## - test_prep:practice_sport 2 289.60 66674 3081.2
## - gender:wkly_study_hours 2 292.89 66678 3081.2
## - lunch_type:parent_marital_status 2 313.74 66698 3081.4
## - parent_educ:parent_marital_status 13 2856.05 69241 3081.5
## - gender:practice_sport 2 329.64 66714 3081.6
## - test_prep:transport_means 1 123.71 66508 3081.7
## - ethnic_group:is_first_child 4 851.65 67236 3082.2
## - ethnic_group:transport_means 4 854.21 67239 3082.2
## - lunch_type:is_first_child 1 178.29 66563 3082.2
## - practice_sport:transport_means 2 413.68 66798 3082.3
## - lunch_type:transport_means 1 210.36 66595 3082.5
## <none> 66385 3082.6
## - is_first_child:transport_means 1 226.07 66611 3082.6
## - test_prep:wkly_study_hours 2 457.36 66842 3082.7
## - practice_sport:wkly_study_hours 4 926.35 67311 3082.8
## - parent_educ:practice_sport 10 2400.56 68785 3083.6
## - parent_educ:is_first_child 5 1378.21 67763 3084.8
## - parent_marital_status:transport_means 3 938.11 67323 3084.9
## - lunch_type:wkly_study_hours 2 734.78 67119 3085.1
## - ethnic_group:parent_marital_status 9 2431.75 68816 3085.8
## - lunch_type:practice_sport 2 1041.78 67426 3087.8
## + gender:parent_marital_status 3 8.49 66376 3088.6
## + ethnic_group:practice_sport 8 1102.72 65282 3088.8
## + parent_educ:lunch_type 5 384.89 66000 3089.2
## + ethnic_group:wkly_study_hours 8 970.65 65414 3089.9
## + parent_educ:test_prep 5 200.85 66184 3090.8
## + parent_educ:wkly_study_hours 10 1239.53 65145 3091.5
## - parent_marital_status:wkly_study_hours 4 2251.07 68636 3094.3
## - parent_marital_status:is_first_child 2 2096.19 68481 3097.0
## + ethnic_group:parent_educ 20 2346.89 64038 3101.4
##
## Step: AIC=3077.59
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:parent_educ +
## gender:lunch_type + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:transport_means 5 543.87 67263 3072.4
## - gender:parent_educ 5 573.95 67293 3072.6
## - ethnic_group:test_prep 4 502.89 67222 3074.0
## - parent_marital_status:practice_sport 4 539.12 67258 3074.3
## - test_prep:parent_marital_status 2 143.84 66863 3074.9
## - is_first_child:wkly_study_hours 2 166.05 66885 3075.1
## - practice_sport:is_first_child 2 168.91 66888 3075.1
## - transport_means:wkly_study_hours 2 184.33 66903 3075.2
## - gender:transport_means 1 0.05 66719 3075.6
## - gender:test_prep 1 4.59 66723 3075.6
## - gender:lunch_type 1 8.88 66728 3075.7
## - ethnic_group:lunch_type 4 701.29 67420 3075.8
## - test_prep:is_first_child 1 27.50 66746 3075.8
## - gender:is_first_child 1 37.57 66756 3075.9
## - lunch_type:test_prep 1 42.48 66761 3076.0
## - test_prep:practice_sport 2 284.58 67003 3076.1
## - lunch_type:parent_marital_status 2 300.95 67020 3076.2
## - gender:practice_sport 2 316.56 67035 3076.4
## - gender:wkly_study_hours 2 323.72 67042 3076.4
## - test_prep:transport_means 1 136.37 66855 3076.8
## - parent_educ:parent_marital_status 13 2927.80 69647 3076.9
## - ethnic_group:is_first_child 4 837.49 67556 3076.9
## - ethnic_group:transport_means 4 843.50 67562 3077.0
## - practice_sport:transport_means 2 404.91 67124 3077.2
## - lunch_type:is_first_child 1 185.14 66904 3077.2
## - lunch_type:transport_means 1 215.15 66934 3077.5
## <none> 66719 3077.6
## - is_first_child:transport_means 1 247.01 66966 3077.8
## - test_prep:wkly_study_hours 2 499.70 67218 3078.0
## - practice_sport:wkly_study_hours 4 963.49 67682 3078.1
## - parent_educ:practice_sport 10 2429.40 69148 3078.7
## - ethnic_group:parent_marital_status 9 2321.43 69040 3079.8
## - parent_marital_status:transport_means 3 952.44 67671 3079.9
## - lunch_type:wkly_study_hours 2 735.88 67455 3080.1
## - parent_educ:is_first_child 5 1473.91 68193 3080.5
## + gender:ethnic_group 4 334.06 66385 3082.6
## + gender:parent_marital_status 3 9.39 66709 3083.5
## - lunch_type:practice_sport 2 1175.07 67894 3083.9
## + parent_educ:lunch_type 5 385.08 66334 3084.2
## + ethnic_group:wkly_study_hours 8 973.05 65746 3084.9
## + ethnic_group:practice_sport 8 962.81 65756 3085.0
## + parent_educ:test_prep 5 159.07 66560 3086.2
## + parent_educ:wkly_study_hours 10 1225.64 65493 3086.7
## - parent_marital_status:wkly_study_hours 4 2289.79 69009 3089.5
## - parent_marital_status:is_first_child 2 2193.29 68912 3092.7
## + ethnic_group:parent_educ 20 2280.02 64439 3097.1
##
## Step: AIC=3072.38
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:parent_educ +
## gender:lunch_type + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_educ 5 579.12 67842 3067.4
## - ethnic_group:test_prep 4 537.48 67800 3069.1
## - parent_marital_status:practice_sport 4 539.25 67802 3069.1
## - test_prep:parent_marital_status 2 134.95 67398 3069.6
## - practice_sport:is_first_child 2 135.32 67398 3069.6
## - is_first_child:wkly_study_hours 2 153.61 67416 3069.7
## - transport_means:wkly_study_hours 2 184.05 67447 3070.0
## - gender:transport_means 1 0.09 67263 3070.4
## - gender:test_prep 1 1.81 67264 3070.4
## - gender:lunch_type 1 15.08 67278 3070.5
## - gender:is_first_child 1 33.95 67297 3070.7
## - gender:wkly_study_hours 2 266.92 67530 3070.7
## - test_prep:is_first_child 1 50.08 67313 3070.8
## - lunch_type:test_prep 1 58.79 67321 3070.9
## - test_prep:practice_sport 2 301.02 67564 3071.0
## - ethnic_group:lunch_type 4 765.58 68028 3071.1
## - practice_sport:transport_means 2 331.21 67594 3071.3
## - parent_educ:parent_marital_status 13 2920.47 70183 3071.5
## - gender:practice_sport 2 354.13 67617 3071.5
## - lunch_type:parent_marital_status 2 356.61 67619 3071.5
## - test_prep:transport_means 1 161.49 67424 3071.8
## - ethnic_group:is_first_child 4 860.27 68123 3071.9
## - lunch_type:is_first_child 1 192.18 67455 3072.1
## - is_first_child:transport_means 1 210.90 67474 3072.2
## - lunch_type:transport_means 1 213.26 67476 3072.2
## <none> 67263 3072.4
## - ethnic_group:transport_means 4 960.94 68224 3072.8
## - test_prep:wkly_study_hours 2 521.24 67784 3072.9
## - parent_educ:practice_sport 10 2393.16 69656 3073.0
## - practice_sport:wkly_study_hours 4 1070.29 68333 3073.7
## - parent_marital_status:transport_means 3 845.76 68108 3073.8
## - parent_educ:is_first_child 5 1453.38 68716 3075.0
## - ethnic_group:parent_marital_status 9 2419.49 69682 3075.2
## - lunch_type:wkly_study_hours 2 855.76 68118 3075.8
## + parent_educ:transport_means 5 543.87 66719 3077.6
## + gender:ethnic_group 4 275.34 66987 3078.0
## + gender:parent_marital_status 3 15.46 67247 3078.2
## + parent_educ:lunch_type 5 384.38 66878 3079.0
## - lunch_type:practice_sport 2 1273.57 68536 3079.4
## + ethnic_group:wkly_study_hours 8 916.36 66346 3080.3
## + parent_educ:test_prep 5 205.37 67057 3080.6
## + ethnic_group:practice_sport 8 878.28 66384 3080.6
## + parent_educ:wkly_study_hours 10 1247.47 66015 3081.3
## - parent_marital_status:wkly_study_hours 4 2322.31 69585 3084.4
## - parent_marital_status:is_first_child 2 2177.48 69440 3087.2
## + ethnic_group:parent_educ 20 2463.59 64799 3090.4
##
## Step: AIC=3067.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:test_prep 4 472.9 68315 3063.5
## - parent_marital_status:practice_sport 4 538.6 68380 3064.1
## - test_prep:parent_marital_status 2 116.3 67958 3064.4
## - practice_sport:is_first_child 2 164.3 68006 3064.9
## - is_first_child:wkly_study_hours 2 175.1 68017 3065.0
## - transport_means:wkly_study_hours 2 188.2 68030 3065.1
## - gender:transport_means 1 0.1 67842 3065.4
## - gender:test_prep 1 1.5 67843 3065.4
## - ethnic_group:lunch_type 4 700.2 68542 3065.5
## - gender:lunch_type 1 16.1 67858 3065.6
## - gender:is_first_child 1 34.3 67876 3065.7
## - gender:wkly_study_hours 2 295.8 68138 3066.0
## - practice_sport:transport_means 2 303.3 68145 3066.1
## - test_prep:is_first_child 1 73.1 67915 3066.1
## - lunch_type:test_prep 1 80.4 67922 3066.1
## - lunch_type:parent_marital_status 2 345.7 68187 3066.4
## - test_prep:practice_sport 2 352.4 68194 3066.5
## - gender:practice_sport 2 362.5 68204 3066.6
## - test_prep:transport_means 1 158.6 68000 3066.8
## - ethnic_group:is_first_child 4 855.9 68698 3066.8
## - is_first_child:transport_means 1 195.1 68037 3067.1
## - lunch_type:is_first_child 1 204.2 68046 3067.2
## <none> 67842 3067.4
## - parent_educ:practice_sport 10 2394.3 70236 3067.9
## - lunch_type:transport_means 1 288.9 68131 3067.9
## - test_prep:wkly_study_hours 2 576.3 68418 3068.4
## - practice_sport:wkly_study_hours 4 1062.6 68904 3068.6
## - parent_educ:is_first_child 5 1333.5 69175 3068.9
## - parent_educ:parent_marital_status 13 3262.6 71104 3069.2
## - ethnic_group:transport_means 4 1140.1 68982 3069.3
## - parent_marital_status:transport_means 3 926.1 68768 3069.4
## - ethnic_group:parent_marital_status 9 2363.8 70206 3069.7
## - lunch_type:wkly_study_hours 2 879.5 68721 3071.0
## + gender:parent_educ 5 579.1 67263 3072.4
## + parent_educ:transport_means 5 549.0 67293 3072.6
## + gender:parent_marital_status 3 4.7 67837 3073.4
## + gender:ethnic_group 4 194.0 67648 3073.8
## + parent_educ:lunch_type 5 343.0 67499 3074.4
## - lunch_type:practice_sport 2 1328.3 69170 3074.9
## + ethnic_group:wkly_study_hours 8 895.6 66946 3075.6
## + parent_educ:test_prep 5 172.0 67670 3075.9
## + ethnic_group:practice_sport 8 845.9 66996 3076.0
## + parent_educ:wkly_study_hours 10 1223.0 66619 3076.7
## - parent_marital_status:wkly_study_hours 4 2407.9 70250 3080.0
## - parent_marital_status:is_first_child 2 2111.7 69953 3081.5
## + ethnic_group:parent_educ 20 2467.1 65375 3085.6
##
## Step: AIC=3063.54
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:practice_sport 4 515.8 68830 3060.0
## - test_prep:parent_marital_status 2 135.4 68450 3060.7
## - ethnic_group:lunch_type 4 622.0 68937 3060.9
## - is_first_child:wkly_study_hours 2 165.2 68480 3061.0
## - transport_means:wkly_study_hours 2 186.3 68501 3061.1
## - practice_sport:is_first_child 2 200.7 68515 3061.3
## - gender:test_prep 1 0.1 68315 3061.5
## - gender:transport_means 1 0.1 68315 3061.5
## - gender:lunch_type 1 9.7 68324 3061.6
## - gender:is_first_child 1 17.5 68332 3061.7
## - test_prep:practice_sport 2 287.2 68602 3062.0
## - test_prep:is_first_child 1 69.2 68384 3062.1
## - gender:wkly_study_hours 2 303.9 68619 3062.2
## - practice_sport:transport_means 2 316.7 68631 3062.3
## - lunch_type:test_prep 1 103.0 68418 3062.4
## - gender:practice_sport 2 362.7 68677 3062.7
## - lunch_type:parent_marital_status 2 373.3 68688 3062.8
## - ethnic_group:is_first_child 4 849.9 69165 3062.8
## - test_prep:transport_means 1 196.2 68511 3063.2
## - is_first_child:transport_means 1 200.9 68515 3063.3
## - lunch_type:is_first_child 1 207.4 68522 3063.3
## <none> 68315 3063.5
## - parent_educ:practice_sport 10 2386.3 70701 3063.8
## - lunch_type:transport_means 1 325.6 68640 3064.3
## - practice_sport:wkly_study_hours 4 1079.2 69394 3064.8
## - parent_educ:is_first_child 5 1328.6 69643 3064.9
## - test_prep:wkly_study_hours 2 642.6 68957 3065.1
## - parent_educ:parent_marital_status 13 3270.8 71585 3065.1
## - parent_marital_status:transport_means 3 893.5 69208 3065.2
## - ethnic_group:parent_marital_status 9 2398.8 70713 3065.9
## - ethnic_group:transport_means 4 1216.2 69531 3065.9
## - lunch_type:wkly_study_hours 2 883.9 69199 3067.1
## + ethnic_group:test_prep 4 472.9 67842 3067.4
## + parent_educ:transport_means 5 580.8 67734 3068.5
## + gender:parent_educ 5 514.5 67800 3069.1
## + gender:parent_marital_status 3 4.7 68310 3069.5
## + gender:ethnic_group 4 157.4 68157 3070.2
## + parent_educ:lunch_type 5 352.3 67962 3070.5
## + ethnic_group:wkly_study_hours 8 891.3 67423 3071.8
## - lunch_type:practice_sport 2 1447.4 69762 3071.9
## + ethnic_group:practice_sport 8 870.0 67445 3072.0
## + parent_educ:wkly_study_hours 10 1235.0 67080 3072.8
## + parent_educ:test_prep 5 87.1 68228 3072.8
## - parent_marital_status:wkly_study_hours 4 2256.3 70571 3074.7
## - parent_marital_status:is_first_child 2 2108.8 70423 3077.5
## + ethnic_group:parent_educ 20 2467.3 65847 3081.8
##
## Step: AIC=3059.97
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:parent_marital_status 2 118.5 68949 3057.0
## - practice_sport:is_first_child 2 135.1 68966 3057.1
## - lunch_type:parent_marital_status 3 380.8 69211 3057.2
## - transport_means:wkly_study_hours 2 180.1 69011 3057.5
## - is_first_child:wkly_study_hours 2 208.2 69039 3057.8
## - ethnic_group:lunch_type 4 693.2 69524 3057.9
## - gender:transport_means 1 0.1 68831 3058.0
## - gender:test_prep 1 1.6 68832 3058.0
## - gender:is_first_child 1 10.6 68841 3058.1
## - gender:lunch_type 1 11.7 68842 3058.1
## - practice_sport:transport_means 2 277.5 69108 3058.3
## - test_prep:practice_sport 2 288.4 69119 3058.4
## - test_prep:is_first_child 1 63.3 68894 3058.5
## - gender:wkly_study_hours 2 335.4 69166 3058.8
## - lunch_type:test_prep 1 108.8 68939 3058.9
## - lunch_type:is_first_child 1 147.8 68978 3059.2
## - ethnic_group:is_first_child 4 868.0 69698 3059.4
## - gender:practice_sport 2 400.2 69231 3059.4
## - test_prep:transport_means 1 173.0 69003 3059.5
## - parent_educ:practice_sport 10 2335.4 71166 3059.7
## - is_first_child:transport_means 1 222.7 69053 3059.9
## <none> 68830 3060.0
## - lunch_type:transport_means 1 270.9 69101 3060.3
## - ethnic_group:parent_marital_status 10 2412.2 71243 3060.3
## - parent_educ:is_first_child 5 1324.6 70155 3061.2
## - practice_sport:wkly_study_hours 4 1108.8 69939 3061.4
## - parent_marital_status:transport_means 3 877.4 69708 3061.4
## - ethnic_group:transport_means 4 1123.2 69954 3061.5
## - test_prep:wkly_study_hours 2 713.3 69544 3062.1
## - parent_educ:parent_marital_status 14 3646.4 72477 3062.4
## - lunch_type:wkly_study_hours 2 867.7 69698 3063.4
## + parent_marital_status:practice_sport 4 515.8 68315 3063.5
## + ethnic_group:test_prep 4 450.1 68380 3064.1
## + parent_educ:transport_means 5 597.6 68233 3064.8
## + gender:parent_educ 5 512.3 68318 3065.6
## + gender:parent_marital_status 3 3.7 68827 3065.9
## + gender:ethnic_group 4 171.0 68659 3066.5
## + parent_educ:lunch_type 5 376.4 68454 3066.7
## + ethnic_group:practice_sport 8 991.3 67839 3067.4
## - lunch_type:practice_sport 2 1394.4 70225 3067.8
## + parent_educ:wkly_study_hours 10 1326.5 67504 3068.5
## + parent_educ:test_prep 5 91.2 68739 3069.2
## + ethnic_group:wkly_study_hours 8 764.8 68066 3069.4
## - parent_marital_status:wkly_study_hours 5 2336.3 71167 3069.7
## - parent_marital_status:is_first_child 2 2343.8 71174 3075.7
## + ethnic_group:parent_educ 20 2528.6 66302 3077.9
##
## Step: AIC=3056.99
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:parent_marital_status 3 363.1 69312 3054.1
## - practice_sport:is_first_child 2 128.7 69078 3054.1
## - transport_means:wkly_study_hours 2 187.6 69137 3054.6
## - is_first_child:wkly_study_hours 2 219.9 69169 3054.9
## - gender:transport_means 1 0.0 68949 3055.0
## - gender:test_prep 1 0.9 68950 3055.0
## - ethnic_group:lunch_type 4 708.8 69658 3055.0
## - gender:is_first_child 1 12.3 68961 3055.1
## - gender:lunch_type 1 13.4 68962 3055.1
## - practice_sport:transport_means 2 279.0 69228 3055.4
## - test_prep:practice_sport 2 309.6 69259 3055.6
## - test_prep:is_first_child 1 81.0 69030 3055.7
## - gender:wkly_study_hours 2 339.7 69289 3055.9
## - ethnic_group:parent_marital_status 11 2493.0 71442 3055.9
## - lunch_type:test_prep 1 116.7 69066 3056.0
## - lunch_type:is_first_child 1 130.3 69079 3056.1
## - gender:practice_sport 2 390.2 69339 3056.3
## - test_prep:transport_means 1 190.2 69139 3056.6
## - parent_educ:practice_sport 10 2364.1 71313 3056.9
## - is_first_child:transport_means 1 221.4 69170 3056.9
## <none> 68949 3057.0
## - ethnic_group:is_first_child 4 941.5 69890 3057.0
## - lunch_type:transport_means 1 271.5 69221 3057.3
## - practice_sport:wkly_study_hours 4 1068.4 70017 3058.1
## - parent_educ:parent_marital_status 15 3736.4 72685 3058.1
## - parent_educ:is_first_child 5 1326.1 70275 3058.2
## - ethnic_group:transport_means 4 1133.8 70083 3058.6
## - parent_marital_status:transport_means 3 949.4 69898 3059.1
## - test_prep:wkly_study_hours 2 717.9 69667 3059.1
## + test_prep:parent_marital_status 2 118.5 68830 3060.0
## - lunch_type:wkly_study_hours 2 854.3 69803 3060.3
## + parent_marital_status:practice_sport 4 498.9 68450 3060.7
## + ethnic_group:test_prep 4 471.9 68477 3060.9
## + parent_educ:transport_means 5 594.1 68355 3061.9
## + gender:parent_educ 5 487.7 68461 3062.8
## + gender:parent_marital_status 3 3.2 68946 3063.0
## + gender:ethnic_group 4 173.1 68776 3063.5
## + parent_educ:lunch_type 5 381.0 68568 3063.7
## + ethnic_group:practice_sport 8 1010.9 67938 3064.3
## - lunch_type:practice_sport 2 1364.2 70313 3064.6
## + parent_educ:wkly_study_hours 10 1310.2 67639 3065.7
## + ethnic_group:wkly_study_hours 8 808.1 68141 3066.0
## + parent_educ:test_prep 5 83.1 68866 3066.3
## - parent_marital_status:wkly_study_hours 6 2636.8 71586 3067.1
## - parent_marital_status:is_first_child 3 2492.4 71441 3071.9
## + ethnic_group:parent_educ 20 2530.7 66418 3074.9
##
## Step: AIC=3054.09
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:is_first_child 2 102.1 69414 3051.0
## - is_first_child:wkly_study_hours 2 207.0 69519 3051.8
## - ethnic_group:parent_marital_status 11 2366.0 71678 3051.9
## - transport_means:wkly_study_hours 2 212.7 69525 3051.9
## - gender:transport_means 1 1.3 69313 3052.1
## - gender:test_prep 1 3.7 69316 3052.1
## - ethnic_group:lunch_type 4 722.5 70035 3052.2
## - gender:is_first_child 1 19.3 69331 3052.2
## - gender:lunch_type 1 29.1 69341 3052.3
## - practice_sport:transport_means 2 265.1 69577 3052.3
## - gender:wkly_study_hours 2 288.0 69600 3052.5
## - test_prep:is_first_child 1 76.6 69389 3052.7
## - test_prep:practice_sport 2 327.5 69640 3052.9
## - gender:practice_sport 2 339.9 69652 3053.0
## - lunch_type:test_prep 1 110.6 69423 3053.0
## - lunch_type:is_first_child 1 118.9 69431 3053.1
## - parent_educ:practice_sport 10 2314.2 71626 3053.5
## - ethnic_group:is_first_child 4 882.6 70195 3053.6
## - test_prep:transport_means 1 191.4 69503 3053.7
## <none> 69312 3054.1
## - is_first_child:transport_means 1 236.1 69548 3054.1
## - lunch_type:transport_means 1 283.0 69595 3054.5
## - practice_sport:wkly_study_hours 4 1043.8 70356 3054.9
## - parent_educ:is_first_child 5 1292.5 70605 3055.0
## - ethnic_group:transport_means 4 1109.2 70421 3055.5
## - parent_educ:parent_marital_status 15 3835.0 73147 3055.9
## - parent_marital_status:transport_means 3 935.7 70248 3056.0
## - test_prep:wkly_study_hours 2 703.5 70016 3056.1
## - lunch_type:wkly_study_hours 2 778.6 70091 3056.7
## + lunch_type:parent_marital_status 3 363.1 68949 3057.0
## + test_prep:parent_marital_status 2 100.8 69211 3057.2
## + ethnic_group:test_prep 4 502.5 68810 3057.8
## + parent_educ:transport_means 5 651.6 68660 3058.5
## + parent_marital_status:practice_sport 5 507.8 68804 3059.8
## + gender:parent_marital_status 3 19.6 69293 3059.9
## + gender:parent_educ 5 471.7 68840 3060.1
## + gender:ethnic_group 4 167.2 69145 3060.7
## - lunch_type:practice_sport 2 1267.6 70580 3060.8
## + parent_educ:lunch_type 5 356.7 68955 3061.0
## + ethnic_group:practice_sport 8 1016.1 68296 3061.4
## + parent_educ:wkly_study_hours 10 1340.9 67971 3062.6
## + ethnic_group:wkly_study_hours 8 789.2 68523 3063.3
## - parent_marital_status:wkly_study_hours 6 2550.9 71863 3063.4
## + parent_educ:test_prep 5 50.5 69262 3063.7
## - parent_marital_status:is_first_child 3 2435.5 71748 3068.5
## + ethnic_group:parent_educ 20 2270.2 67042 3074.4
##
## Step: AIC=3050.96
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_marital_status 11 2305.2 71719 3048.2
## - is_first_child:wkly_study_hours 2 191.9 69606 3048.6
## - transport_means:wkly_study_hours 2 205.6 69620 3048.7
## - practice_sport:transport_means 2 236.5 69651 3049.0
## - gender:transport_means 1 2.8 69417 3049.0
## - gender:test_prep 1 5.6 69420 3049.0
## - ethnic_group:lunch_type 4 724.5 70139 3049.1
## - gender:is_first_child 1 23.6 69438 3049.2
## - gender:lunch_type 1 38.5 69453 3049.3
## - test_prep:is_first_child 1 52.7 69467 3049.4
## - gender:wkly_study_hours 2 289.2 69703 3049.4
## - gender:practice_sport 2 343.5 69758 3049.9
## - test_prep:practice_sport 2 349.8 69764 3049.9
## - parent_educ:practice_sport 10 2272.3 71686 3050.0
## - lunch_type:test_prep 1 128.0 69542 3050.0
## - lunch_type:is_first_child 1 131.7 69546 3050.1
## - test_prep:transport_means 1 191.5 69606 3050.6
## - ethnic_group:is_first_child 4 907.0 70321 3050.6
## <none> 69414 3051.0
## - lunch_type:transport_means 1 270.0 69684 3051.2
## - is_first_child:transport_means 1 271.7 69686 3051.3
## - parent_educ:is_first_child 5 1261.5 70676 3051.6
## - ethnic_group:transport_means 4 1065.9 70480 3051.9
## - practice_sport:wkly_study_hours 4 1075.9 70490 3052.0
## - parent_educ:parent_marital_status 15 3782.3 73197 3052.3
## - parent_marital_status:transport_means 3 901.5 70316 3052.6
## - test_prep:wkly_study_hours 2 673.0 70087 3052.7
## - lunch_type:wkly_study_hours 2 782.5 70197 3053.6
## + practice_sport:is_first_child 2 102.1 69312 3054.1
## + lunch_type:parent_marital_status 3 336.6 69078 3054.1
## + test_prep:parent_marital_status 2 97.8 69316 3054.1
## + ethnic_group:test_prep 4 524.0 68890 3054.5
## + parent_educ:transport_means 5 604.0 68810 3055.8
## + gender:parent_marital_status 3 18.0 69396 3056.8
## + gender:parent_educ 5 484.2 68930 3056.8
## + parent_marital_status:practice_sport 5 446.7 68968 3057.2
## - lunch_type:practice_sport 2 1235.0 70649 3057.4
## + gender:ethnic_group 4 187.0 69227 3057.4
## + parent_educ:lunch_type 5 356.3 69058 3057.9
## + ethnic_group:practice_sport 8 949.0 68465 3058.8
## + parent_educ:wkly_study_hours 10 1293.2 68121 3059.9
## + ethnic_group:wkly_study_hours 8 799.5 68615 3060.1
## - parent_marital_status:wkly_study_hours 6 2548.9 71963 3060.2
## + parent_educ:test_prep 5 54.2 69360 3060.5
## - parent_marital_status:is_first_child 3 2469.3 71884 3065.6
## + ethnic_group:parent_educ 20 2240.2 67174 3071.6
##
## Step: AIC=3048.23
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:practice_sport 10 1945.7 73665 3044.0
## - practice_sport:transport_means 2 95.5 71815 3045.0
## - ethnic_group:is_first_child 4 586.8 72306 3045.0
## - transport_means:wkly_study_hours 2 160.4 71880 3045.6
## - is_first_child:wkly_study_hours 2 167.1 71886 3045.6
## - gender:wkly_study_hours 2 199.5 71919 3045.9
## - ethnic_group:lunch_type 4 741.3 72461 3046.3
## - gender:transport_means 1 24.5 71744 3046.4
## - gender:test_prep 1 37.7 71757 3046.5
## - test_prep:is_first_child 1 40.0 71759 3046.6
## - gender:lunch_type 1 42.6 71762 3046.6
## - gender:is_first_child 1 52.0 71771 3046.7
## - test_prep:practice_sport 2 296.9 72016 3046.7
## - gender:practice_sport 2 338.7 72058 3047.0
## - lunch_type:test_prep 1 98.2 71818 3047.0
## - lunch_type:is_first_child 1 98.2 71818 3047.0
## - test_prep:transport_means 1 173.5 71893 3047.7
## - parent_educ:is_first_child 5 1201.7 72921 3048.0
## <none> 71719 3048.2
## - parent_marital_status:transport_means 3 741.3 72461 3048.3
## - practice_sport:wkly_study_hours 4 990.2 72710 3048.3
## - lunch_type:transport_means 1 320.0 72039 3048.9
## - is_first_child:transport_means 1 356.3 72076 3049.2
## - ethnic_group:transport_means 4 1128.0 72847 3049.4
## - lunch_type:wkly_study_hours 2 705.8 72425 3050.0
## - parent_educ:parent_marital_status 15 3998.6 75718 3050.2
## - test_prep:wkly_study_hours 2 820.6 72540 3050.9
## + ethnic_group:parent_marital_status 11 2305.2 69414 3051.0
## + ethnic_group:test_prep 4 586.9 71132 3051.4
## + practice_sport:is_first_child 2 41.3 71678 3051.9
## - parent_marital_status:wkly_study_hours 6 1941.0 73660 3052.0
## + parent_educ:transport_means 5 747.1 70972 3052.1
## + lunch_type:parent_marital_status 3 219.1 71500 3052.4
## + test_prep:parent_marital_status 3 147.7 71572 3053.0
## + gender:parent_marital_status 3 84.7 71635 3053.5
## + gender:parent_educ 5 442.4 71277 3054.6
## - lunch_type:practice_sport 2 1319.4 73039 3055.0
## + gender:ethnic_group 4 146.6 71573 3055.0
## + parent_educ:lunch_type 5 373.5 71346 3055.2
## + parent_marital_status:practice_sport 6 525.2 71194 3055.9
## + parent_educ:wkly_study_hours 10 1465.5 70254 3056.1
## + ethnic_group:practice_sport 8 879.1 70840 3057.0
## + parent_educ:test_prep 5 50.8 71669 3057.8
## + ethnic_group:wkly_study_hours 8 747.7 70972 3058.1
## - parent_marital_status:is_first_child 3 2272.4 73992 3060.6
## + ethnic_group:parent_educ 20 2384.6 69335 3068.3
##
## Step: AIC=3044.03
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:is_first_child 4 616.0 74281 3040.9
## - practice_sport:transport_means 2 114.9 73780 3040.9
## - transport_means:wkly_study_hours 2 119.6 73785 3041.0
## - is_first_child:wkly_study_hours 2 175.7 73841 3041.4
## - ethnic_group:lunch_type 4 736.1 74401 3041.9
## - gender:wkly_study_hours 2 246.2 73911 3042.0
## - gender:lunch_type 1 26.0 73691 3042.2
## - gender:practice_sport 2 279.5 73945 3042.3
## - test_prep:is_first_child 1 51.2 73716 3042.4
## - gender:transport_means 1 53.1 73718 3042.4
## - gender:test_prep 1 56.7 73722 3042.5
## - gender:is_first_child 1 66.4 73731 3042.6
## - lunch_type:is_first_child 1 79.2 73744 3042.7
## - test_prep:practice_sport 2 349.4 74014 3042.8
## - lunch_type:test_prep 1 121.2 73786 3043.0
## - practice_sport:wkly_study_hours 4 879.5 74545 3043.0
## - test_prep:transport_means 1 145.6 73811 3043.2
## <none> 73665 3044.0
## - is_first_child:transport_means 1 260.1 73925 3044.1
## - lunch_type:transport_means 1 285.2 73950 3044.3
## - parent_educ:is_first_child 5 1425.4 75090 3045.3
## - ethnic_group:transport_means 4 1173.7 74839 3045.3
## - test_prep:wkly_study_hours 2 674.2 74339 3045.4
## - parent_marital_status:transport_means 3 930.7 74596 3045.4
## - lunch_type:wkly_study_hours 2 751.1 74416 3046.0
## + ethnic_group:test_prep 4 596.7 73068 3047.2
## + practice_sport:is_first_child 2 23.4 73642 3047.8
## - parent_educ:parent_marital_status 15 4352.1 78017 3047.9
## - parent_marital_status:wkly_study_hours 6 2020.8 75686 3048.0
## + parent_educ:practice_sport 10 1945.7 71719 3048.2
## + lunch_type:parent_marital_status 3 173.9 73491 3048.6
## + test_prep:parent_marital_status 3 155.5 73510 3048.8
## - lunch_type:practice_sport 2 1103.6 74769 3048.8
## + parent_educ:transport_means 5 643.4 73022 3048.8
## + gender:parent_marital_status 3 77.3 73588 3049.4
## + ethnic_group:parent_marital_status 11 1978.6 71686 3050.0
## + gender:ethnic_group 4 239.4 73426 3050.1
## + gender:parent_educ 5 474.1 73191 3050.2
## + parent_educ:wkly_study_hours 10 1601.0 72064 3051.1
## + parent_educ:lunch_type 5 343.0 73322 3051.3
## + parent_marital_status:practice_sport 6 420.8 73244 3052.6
## + ethnic_group:practice_sport 8 895.6 72769 3052.8
## + parent_educ:test_prep 5 96.6 73568 3053.2
## + ethnic_group:wkly_study_hours 8 768.5 72897 3053.8
## - parent_marital_status:is_first_child 3 2307.1 75972 3056.2
## + ethnic_group:parent_educ 20 2365.9 71299 3064.8
##
## Step: AIC=3040.94
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:lunch_type 4 559.7 74841 3037.4
## - practice_sport:transport_means 2 104.8 74386 3037.8
## - transport_means:wkly_study_hours 2 126.4 74407 3037.9
## - gender:wkly_study_hours 2 196.4 74477 3038.5
## - is_first_child:wkly_study_hours 2 229.6 74511 3038.8
## - gender:practice_sport 2 251.9 74533 3038.9
## - gender:lunch_type 1 14.3 74295 3039.1
## - gender:is_first_child 1 30.8 74312 3039.2
## - gender:test_prep 1 40.0 74321 3039.3
## - gender:transport_means 1 58.5 74340 3039.4
## - test_prep:is_first_child 1 75.8 74357 3039.5
## - test_prep:practice_sport 2 350.0 74631 3039.7
## - test_prep:transport_means 1 115.1 74396 3039.8
## - lunch_type:is_first_child 1 119.2 74400 3039.9
## - practice_sport:wkly_study_hours 4 880.0 75161 3039.9
## - is_first_child:transport_means 1 144.6 74426 3040.1
## - lunch_type:test_prep 1 149.4 74430 3040.1
## <none> 74281 3040.9
## - lunch_type:transport_means 1 261.8 74543 3041.0
## - test_prep:wkly_study_hours 2 522.3 74803 3041.1
## - parent_marital_status:transport_means 3 939.6 75221 3042.3
## - lunch_type:wkly_study_hours 2 692.9 74974 3042.4
## - parent_educ:is_first_child 5 1465.0 75746 3042.5
## - ethnic_group:transport_means 4 1307.4 75588 3043.2
## - parent_educ:parent_marital_status 15 4239.6 78521 3043.7
## + ethnic_group:is_first_child 4 616.0 73665 3044.0
## + ethnic_group:test_prep 4 581.5 73700 3044.3
## - parent_marital_status:wkly_study_hours 6 1978.0 76259 3044.4
## + practice_sport:is_first_child 2 40.8 74240 3044.6
## + parent_educ:practice_sport 10 1974.9 72306 3045.0
## + test_prep:parent_marital_status 3 184.2 74097 3045.5
## - lunch_type:practice_sport 2 1103.4 75384 3045.6
## + lunch_type:parent_marital_status 3 140.1 74141 3045.8
## + parent_educ:transport_means 5 610.0 73671 3046.1
## + gender:parent_marital_status 3 67.0 74214 3046.4
## + gender:ethnic_group 4 192.3 74089 3047.4
## + gender:parent_educ 5 422.0 73859 3047.6
## + parent_educ:wkly_study_hours 10 1654.5 72627 3047.7
## + parent_educ:lunch_type 5 349.3 73932 3048.2
## + ethnic_group:parent_marital_status 11 1673.1 72608 3049.5
## + parent_marital_status:practice_sport 6 385.1 73896 3049.9
## + parent_educ:test_prep 5 113.8 74167 3050.0
## + ethnic_group:practice_sport 8 857.0 73424 3050.1
## + ethnic_group:wkly_study_hours 8 741.7 73539 3051.0
## - parent_marital_status:is_first_child 3 2299.8 76581 3052.9
## + ethnic_group:parent_educ 20 2402.3 71879 3061.5
##
## Step: AIC=3037.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 90.2 74931 3034.1
## - transport_means:wkly_study_hours 2 140.4 74981 3034.5
## - gender:wkly_study_hours 2 204.9 75046 3035.0
## - gender:practice_sport 2 215.5 75056 3035.1
## - is_first_child:wkly_study_hours 2 223.2 75064 3035.1
## - gender:lunch_type 1 15.2 74856 3035.5
## - practice_sport:wkly_study_hours 4 784.5 75625 3035.5
## - gender:is_first_child 1 33.8 74875 3035.6
## - gender:test_prep 1 48.7 74889 3035.8
## - gender:transport_means 1 52.5 74893 3035.8
## - test_prep:is_first_child 1 66.9 74908 3035.9
## - lunch_type:is_first_child 1 106.1 74947 3036.2
## - test_prep:transport_means 1 128.1 74969 3036.4
## - is_first_child:transport_means 1 137.8 74979 3036.4
## - test_prep:practice_sport 2 407.4 75248 3036.6
## - lunch_type:test_prep 1 182.2 75023 3036.8
## <none> 74841 3037.4
## - test_prep:wkly_study_hours 2 520.3 75361 3037.5
## - lunch_type:transport_means 1 325.7 75166 3037.9
## - parent_educ:parent_marital_status 15 4029.3 78870 3038.3
## - lunch_type:wkly_study_hours 2 641.3 75482 3038.4
## - parent_marital_status:transport_means 3 902.6 75743 3038.4
## - ethnic_group:transport_means 4 1226.6 76067 3039.0
## - parent_educ:is_first_child 5 1535.8 76377 3039.3
## + ethnic_group:lunch_type 4 559.7 74281 3040.9
## + practice_sport:is_first_child 2 47.5 74793 3041.0
## - parent_marital_status:wkly_study_hours 6 2059.5 76900 3041.4
## + ethnic_group:test_prep 4 468.2 74373 3041.7
## + parent_educ:practice_sport 10 1964.0 72877 3041.7
## + test_prep:parent_marital_status 3 192.8 74648 3041.8
## + ethnic_group:is_first_child 4 439.7 74401 3041.9
## + parent_educ:transport_means 5 683.2 74158 3042.0
## + lunch_type:parent_marital_status 3 164.7 74676 3042.1
## + gender:parent_marital_status 3 61.4 74779 3042.9
## - lunch_type:practice_sport 2 1228.5 76069 3043.0
## + gender:ethnic_group 4 211.7 74629 3043.7
## + parent_educ:lunch_type 5 391.3 74449 3044.3
## + gender:parent_educ 5 376.2 74465 3044.4
## + parent_marital_status:practice_sport 6 466.6 74374 3045.7
## + ethnic_group:practice_sport 8 965.1 73876 3045.7
## + ethnic_group:parent_marital_status 11 1696.6 73144 3045.8
## + parent_educ:wkly_study_hours 10 1444.5 73396 3045.9
## + parent_educ:test_prep 5 122.2 74719 3046.4
## + ethnic_group:wkly_study_hours 8 794.9 74046 3047.1
## - parent_marital_status:is_first_child 3 2267.8 77109 3049.0
## + ethnic_group:parent_educ 20 2517.8 72323 3057.2
##
## Step: AIC=3034.08
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 152.6 75084 3031.3
## - gender:practice_sport 2 202.8 75134 3031.7
## - gender:wkly_study_hours 2 209.1 75140 3031.7
## - is_first_child:wkly_study_hours 2 215.6 75147 3031.8
## - practice_sport:wkly_study_hours 4 763.7 75695 3032.1
## - gender:lunch_type 1 15.9 74947 3032.2
## - gender:is_first_child 1 39.1 74970 3032.4
## - gender:test_prep 1 46.4 74977 3032.4
## - gender:transport_means 1 52.6 74984 3032.5
## - test_prep:is_first_child 1 65.8 74997 3032.6
## - lunch_type:is_first_child 1 113.8 75045 3033.0
## - test_prep:transport_means 1 124.1 75055 3033.1
## - test_prep:practice_sport 2 399.1 75330 3033.2
## - is_first_child:transport_means 1 157.6 75089 3033.3
## - lunch_type:test_prep 1 200.4 75131 3033.7
## <none> 74931 3034.1
## - test_prep:wkly_study_hours 2 521.1 75452 3034.2
## - lunch_type:transport_means 1 334.9 75266 3034.7
## - parent_educ:parent_marital_status 15 4028.6 78960 3035.0
## - lunch_type:wkly_study_hours 2 635.2 75566 3035.1
## - parent_marital_status:transport_means 3 917.6 75849 3035.3
## - ethnic_group:transport_means 4 1237.8 76169 3035.8
## - parent_educ:is_first_child 5 1530.9 76462 3036.0
## + practice_sport:transport_means 2 90.2 74841 3037.4
## + ethnic_group:lunch_type 4 545.2 74386 3037.8
## + practice_sport:is_first_child 2 36.5 74894 3037.8
## - parent_marital_status:wkly_study_hours 6 2071.5 77003 3038.2
## + parent_educ:practice_sport 10 1980.6 72950 3038.3
## + ethnic_group:test_prep 4 468.3 74463 3038.4
## + test_prep:parent_marital_status 3 193.8 74737 3038.6
## + ethnic_group:is_first_child 4 436.2 74495 3038.6
## + lunch_type:parent_marital_status 3 164.8 74766 3038.8
## + parent_educ:transport_means 5 623.6 74307 3039.2
## - lunch_type:practice_sport 2 1207.3 76138 3039.5
## + gender:parent_marital_status 3 49.0 74882 3039.7
## + gender:ethnic_group 4 211.2 74720 3040.4
## + parent_educ:lunch_type 5 407.0 74524 3040.9
## + gender:parent_educ 5 361.2 74570 3041.2
## + parent_marital_status:practice_sport 6 464.0 74467 3042.4
## + ethnic_group:practice_sport 8 951.2 73980 3042.5
## + parent_educ:test_prep 5 126.5 74805 3043.1
## + ethnic_group:parent_marital_status 11 1608.8 73322 3043.3
## + parent_educ:wkly_study_hours 10 1355.5 73576 3043.3
## + ethnic_group:wkly_study_hours 8 794.8 74136 3043.8
## - parent_marital_status:is_first_child 3 2227.1 77158 3045.4
## + ethnic_group:parent_educ 20 2387.1 72544 3055.0
##
## Step: AIC=3031.28
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:wkly_study_hours 2 200.3 75284 3028.8
## - gender:practice_sport 2 213.6 75297 3029.0
## - is_first_child:wkly_study_hours 2 235.6 75319 3029.1
## - practice_sport:wkly_study_hours 4 769.9 75854 3029.3
## - gender:lunch_type 1 13.4 75097 3029.4
## - gender:is_first_child 1 36.5 75120 3029.6
## - gender:test_prep 1 36.9 75121 3029.6
## - gender:transport_means 1 52.0 75136 3029.7
## - test_prep:is_first_child 1 73.0 75157 3029.8
## - test_prep:transport_means 1 106.3 75190 3030.1
## - lunch_type:is_first_child 1 117.0 75201 3030.2
## - is_first_child:transport_means 1 155.5 75239 3030.5
## - test_prep:practice_sport 2 432.0 75516 3030.7
## - lunch_type:test_prep 1 202.7 75286 3030.9
## - test_prep:wkly_study_hours 2 502.3 75586 3031.2
## <none> 75084 3031.3
## - lunch_type:transport_means 1 316.8 75400 3031.8
## - parent_educ:parent_marital_status 15 4009.8 79093 3032.0
## - parent_marital_status:transport_means 3 899.1 75983 3032.3
## - lunch_type:wkly_study_hours 2 642.7 75726 3032.3
## - parent_educ:is_first_child 5 1516.3 76600 3033.1
## - ethnic_group:transport_means 4 1313.2 76397 3033.5
## + transport_means:wkly_study_hours 2 152.6 74931 3034.1
## + practice_sport:transport_means 2 102.4 74981 3034.5
## + ethnic_group:lunch_type 4 557.6 74526 3034.9
## + practice_sport:is_first_child 2 38.3 75045 3035.0
## + ethnic_group:test_prep 4 478.7 74605 3035.5
## - parent_marital_status:wkly_study_hours 6 2093.8 77177 3035.5
## + test_prep:parent_marital_status 3 190.2 74893 3035.8
## + ethnic_group:is_first_child 4 437.3 74646 3035.8
## + parent_educ:practice_sport 10 1938.5 73145 3035.8
## + lunch_type:parent_marital_status 3 176.1 74908 3035.9
## + parent_educ:transport_means 5 615.5 74468 3036.4
## - lunch_type:practice_sport 2 1206.4 76290 3036.7
## + gender:parent_marital_status 3 42.7 75041 3036.9
## + gender:ethnic_group 4 235.5 74848 3037.4
## + parent_educ:lunch_type 5 412.6 74671 3038.0
## + gender:parent_educ 5 381.1 74703 3038.3
## + ethnic_group:practice_sport 8 981.1 74103 3039.5
## + parent_marital_status:practice_sport 6 470.9 74613 3039.6
## + parent_educ:test_prep 5 132.3 74951 3040.2
## + parent_educ:wkly_study_hours 10 1382.8 73701 3040.3
## + ethnic_group:parent_marital_status 11 1599.1 73485 3040.6
## + ethnic_group:wkly_study_hours 8 685.4 74398 3041.9
## - parent_marital_status:is_first_child 3 2151.3 77235 3041.9
## + ethnic_group:parent_educ 20 2409.9 72674 3052.0
##
## Step: AIC=3028.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - is_first_child:wkly_study_hours 2 224.7 75509 3026.6
## - gender:practice_sport 2 227.7 75512 3026.6
## - practice_sport:wkly_study_hours 4 746.4 76030 3026.7
## - gender:lunch_type 1 9.6 75293 3026.9
## - gender:is_first_child 1 35.4 75319 3027.1
## - gender:test_prep 1 54.5 75338 3027.3
## - gender:transport_means 1 55.2 75339 3027.3
## - test_prep:is_first_child 1 91.8 75376 3027.6
## - lunch_type:is_first_child 1 110.5 75394 3027.7
## - test_prep:transport_means 1 115.1 75399 3027.8
## - is_first_child:transport_means 1 143.5 75427 3028.0
## - test_prep:practice_sport 2 412.6 75696 3028.1
## - lunch_type:test_prep 1 200.7 75485 3028.4
## - test_prep:wkly_study_hours 2 501.3 75785 3028.8
## <none> 75284 3028.8
## - lunch_type:transport_means 1 311.9 75596 3029.3
## - lunch_type:wkly_study_hours 2 588.5 75872 3029.4
## - parent_educ:parent_marital_status 15 4077.9 79362 3030.0
## - parent_marital_status:transport_means 3 918.3 76202 3030.0
## - parent_educ:is_first_child 5 1504.4 76788 3030.5
## - ethnic_group:transport_means 4 1307.8 76592 3031.0
## + gender:wkly_study_hours 2 200.3 75084 3031.3
## + transport_means:wkly_study_hours 2 143.7 75140 3031.7
## + practice_sport:transport_means 2 106.7 75177 3032.0
## + ethnic_group:lunch_type 4 564.3 74720 3032.4
## + practice_sport:is_first_child 2 35.0 75249 3032.6
## + ethnic_group:test_prep 4 500.5 74783 3032.9
## + parent_educ:practice_sport 10 1975.2 73309 3033.2
## + test_prep:parent_marital_status 3 190.2 75094 3033.4
## + lunch_type:parent_marital_status 3 151.8 75132 3033.7
## + ethnic_group:is_first_child 4 393.3 74891 3033.8
## - lunch_type:practice_sport 2 1171.7 76456 3034.0
## + parent_educ:transport_means 5 584.3 74700 3034.2
## + gender:parent_marital_status 3 40.2 75244 3034.5
## - parent_marital_status:wkly_study_hours 6 2307.6 77592 3034.7
## + gender:ethnic_group 4 245.5 75038 3034.9
## + gender:parent_educ 5 409.5 74874 3035.6
## + parent_educ:lunch_type 5 400.9 74883 3035.7
## + ethnic_group:practice_sport 8 1028.4 74255 3036.7
## + parent_marital_status:practice_sport 6 482.3 74802 3037.1
## + parent_educ:wkly_study_hours 10 1462.3 73822 3037.3
## + parent_educ:test_prep 5 144.3 75140 3037.7
## + ethnic_group:parent_marital_status 11 1560.9 73723 3038.5
## - parent_marital_status:is_first_child 3 2096.8 77381 3039.1
## + ethnic_group:wkly_study_hours 8 665.0 74619 3039.6
## + ethnic_group:parent_educ 20 2348.0 72936 3050.2
##
## Step: AIC=3026.61
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:practice_sport 2 221.8 75730 3024.3
## - gender:lunch_type 1 8.1 75517 3024.7
## - practice_sport:wkly_study_hours 4 815.9 76325 3024.9
## - gender:is_first_child 1 47.0 75556 3025.0
## - gender:test_prep 1 56.0 75565 3025.1
## - gender:transport_means 1 60.8 75569 3025.1
## - test_prep:is_first_child 1 66.3 75575 3025.1
## - is_first_child:transport_means 1 121.9 75631 3025.6
## - test_prep:practice_sport 2 387.2 75896 3025.6
## - test_prep:transport_means 1 132.1 75641 3025.6
## - lunch_type:is_first_child 1 147.3 75656 3025.8
## - lunch_type:test_prep 1 226.8 75735 3026.4
## - test_prep:wkly_study_hours 2 504.9 76014 3026.5
## <none> 75509 3026.6
## - lunch_type:transport_means 1 315.6 75824 3027.1
## - parent_marital_status:transport_means 3 854.9 76364 3027.2
## - lunch_type:wkly_study_hours 2 599.4 76108 3027.3
## - parent_educ:is_first_child 5 1416.9 76926 3027.6
## - parent_educ:parent_marital_status 15 4118.0 79627 3027.9
## - ethnic_group:transport_means 4 1292.0 76801 3028.6
## + is_first_child:wkly_study_hours 2 224.7 75284 3028.8
## + gender:wkly_study_hours 2 189.4 75319 3029.1
## + transport_means:wkly_study_hours 2 162.2 75346 3029.3
## + practice_sport:transport_means 2 99.0 75410 3029.8
## + ethnic_group:lunch_type 4 561.9 74947 3030.2
## + practice_sport:is_first_child 2 29.1 75480 3030.4
## + ethnic_group:test_prep 4 516.9 74992 3030.6
## + test_prep:parent_marital_status 3 216.2 75292 3030.9
## + parent_educ:practice_sport 10 1970.1 73539 3031.0
## + ethnic_group:is_first_child 4 436.1 75073 3031.2
## + lunch_type:parent_marital_status 3 148.9 75360 3031.4
## + parent_educ:transport_means 5 557.1 74952 3032.2
## + gender:parent_marital_status 3 43.2 75466 3032.3
## + gender:ethnic_group 4 258.6 75250 3032.6
## - lunch_type:practice_sport 2 1314.3 76823 3032.8
## - parent_marital_status:wkly_study_hours 6 2397.4 77906 3033.1
## + gender:parent_educ 5 449.5 75059 3033.1
## + parent_educ:lunch_type 5 402.2 75106 3033.5
## + ethnic_group:practice_sport 8 1054.8 74454 3034.3
## + parent_marital_status:practice_sport 6 535.4 74973 3034.4
## + parent_educ:wkly_study_hours 10 1496.8 74012 3034.8
## + parent_educ:test_prep 5 130.5 75378 3035.6
## - parent_marital_status:is_first_child 3 2033.1 77542 3036.3
## + ethnic_group:parent_marital_status 11 1481.0 74028 3036.9
## + ethnic_group:wkly_study_hours 8 699.9 74809 3037.1
## + ethnic_group:parent_educ 20 2251.9 73257 3048.8
##
## Step: AIC=3024.34
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:is_first_child + gender:transport_means +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 8.4 75739 3022.4
## - test_prep:is_first_child 1 55.9 75786 3022.8
## - gender:is_first_child 1 57.4 75788 3022.8
## - gender:transport_means 1 71.5 75802 3022.9
## - gender:test_prep 1 71.6 75802 3022.9
## - practice_sport:wkly_study_hours 4 886.4 76617 3023.2
## - test_prep:transport_means 1 123.7 75854 3023.3
## - is_first_child:transport_means 1 137.4 75868 3023.4
## - test_prep:practice_sport 2 423.8 76154 3023.6
## - lunch_type:is_first_child 1 180.2 75911 3023.7
## - lunch_type:test_prep 1 217.8 75948 3024.0
## - test_prep:wkly_study_hours 2 495.1 76226 3024.2
## <none> 75730 3024.3
## - parent_marital_status:transport_means 3 814.9 76545 3024.7
## - lunch_type:wkly_study_hours 2 575.3 76306 3024.8
## - lunch_type:transport_means 1 337.3 76068 3025.0
## - parent_educ:is_first_child 5 1435.2 77166 3025.4
## - parent_educ:parent_marital_status 15 4197.3 79928 3026.2
## - ethnic_group:transport_means 4 1300.0 77030 3026.4
## + gender:practice_sport 2 221.8 75509 3026.6
## + is_first_child:wkly_study_hours 2 218.8 75512 3026.6
## + gender:wkly_study_hours 2 202.8 75528 3026.8
## + transport_means:wkly_study_hours 2 172.4 75558 3027.0
## + practice_sport:transport_means 2 85.5 75645 3027.7
## + practice_sport:is_first_child 2 28.3 75702 3028.1
## + ethnic_group:lunch_type 4 527.5 75203 3028.2
## + ethnic_group:test_prep 4 516.9 75214 3028.3
## + test_prep:parent_marital_status 3 200.8 75530 3028.8
## + ethnic_group:is_first_child 4 413.3 75317 3029.1
## + parent_educ:practice_sport 10 1917.0 73813 3029.2
## + lunch_type:parent_marital_status 3 137.0 75593 3029.3
## + parent_educ:transport_means 5 565.9 75165 3029.9
## + gender:parent_marital_status 3 52.3 75678 3029.9
## - parent_marital_status:wkly_study_hours 6 2321.3 78052 3030.2
## + gender:ethnic_group 4 216.3 75514 3030.7
## - lunch_type:practice_sport 2 1351.3 77082 3030.8
## + gender:parent_educ 5 453.1 75277 3030.8
## + parent_educ:lunch_type 5 416.7 75314 3031.1
## + ethnic_group:practice_sport 8 1124.5 74606 3031.5
## + parent_marital_status:practice_sport 6 558.5 75172 3032.0
## + parent_educ:wkly_study_hours 10 1460.2 74270 3032.8
## + parent_educ:test_prep 5 130.2 75600 3033.3
## - parent_marital_status:is_first_child 3 2060.2 77791 3034.2
## + ethnic_group:parent_marital_status 11 1515.3 74215 3034.4
## + ethnic_group:wkly_study_hours 8 702.9 75028 3034.8
## + ethnic_group:parent_educ 20 2304.5 73426 3046.1
##
## Step: AIC=3022.41
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:is_first_child +
## gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 57.0 75796 3020.8
## - test_prep:is_first_child 1 57.1 75796 3020.8
## - gender:test_prep 1 69.1 75808 3020.9
## - gender:transport_means 1 72.9 75812 3021.0
## - practice_sport:wkly_study_hours 4 884.1 76623 3021.2
## - test_prep:transport_means 1 127.3 75866 3021.4
## - is_first_child:transport_means 1 134.3 75873 3021.4
## - test_prep:practice_sport 2 429.7 76169 3021.7
## - lunch_type:is_first_child 1 182.4 75921 3021.8
## - lunch_type:test_prep 1 226.2 75965 3022.2
## - test_prep:wkly_study_hours 2 500.1 76239 3022.3
## <none> 75739 3022.4
## - parent_marital_status:transport_means 3 808.4 76547 3022.7
## - lunch_type:wkly_study_hours 2 572.3 76311 3022.8
## - lunch_type:transport_means 1 345.8 76085 3023.1
## - parent_educ:is_first_child 5 1434.6 77173 3023.5
## - parent_educ:parent_marital_status 15 4194.5 79933 3024.2
## + gender:lunch_type 1 8.4 75730 3024.3
## - ethnic_group:transport_means 4 1313.0 77052 3024.6
## + gender:practice_sport 2 222.1 75517 3024.7
## + is_first_child:wkly_study_hours 2 217.1 75522 3024.7
## + gender:wkly_study_hours 2 199.5 75539 3024.8
## + transport_means:wkly_study_hours 2 170.3 75569 3025.1
## + practice_sport:transport_means 2 85.8 75653 3025.7
## + practice_sport:is_first_child 2 28.3 75711 3026.2
## + ethnic_group:lunch_type 4 527.2 75212 3026.3
## + ethnic_group:test_prep 4 519.0 75220 3026.3
## + test_prep:parent_marital_status 3 203.5 75535 3026.8
## + ethnic_group:is_first_child 4 409.1 75330 3027.2
## + lunch_type:parent_marital_status 3 142.1 75597 3027.3
## + parent_educ:practice_sport 10 1903.8 73835 3027.4
## + parent_educ:transport_means 5 572.4 75166 3027.9
## + gender:parent_marital_status 3 51.1 75688 3028.0
## - parent_marital_status:wkly_study_hours 6 2359.0 78098 3028.5
## + gender:ethnic_group 4 216.1 75523 3028.7
## + gender:parent_educ 5 450.2 75289 3028.9
## + parent_educ:lunch_type 5 424.1 75315 3029.1
## - lunch_type:practice_sport 2 1386.6 77125 3029.1
## + ethnic_group:practice_sport 8 1102.7 74636 3029.8
## + parent_marital_status:practice_sport 6 554.6 75184 3030.1
## + parent_educ:wkly_study_hours 10 1456.2 74283 3030.9
## + parent_educ:test_prep 5 128.7 75610 3031.4
## - parent_marital_status:is_first_child 3 2051.8 77791 3032.2
## + ethnic_group:parent_marital_status 11 1513.5 74225 3032.5
## + ethnic_group:wkly_study_hours 8 705.0 75034 3032.9
## + ethnic_group:parent_educ 20 2265.2 73474 3044.5
##
## Step: AIC=3020.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:transport_means +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 63.1 75859 3019.3
## - test_prep:is_first_child 1 65.8 75862 3019.4
## - gender:transport_means 1 71.8 75868 3019.4
## - is_first_child:transport_means 1 124.6 75921 3019.8
## - test_prep:transport_means 1 129.3 75925 3019.8
## - practice_sport:wkly_study_hours 4 920.1 76716 3020.0
## - test_prep:practice_sport 2 414.2 76210 3020.1
## - lunch_type:is_first_child 1 171.5 75967 3020.2
## - test_prep:wkly_study_hours 2 490.6 76286 3020.7
## - lunch_type:test_prep 1 235.7 76032 3020.7
## <none> 75796 3020.8
## - lunch_type:wkly_study_hours 2 573.9 76370 3021.3
## - parent_marital_status:transport_means 3 837.6 76634 3021.3
## - lunch_type:transport_means 1 365.6 76161 3021.7
## - parent_educ:is_first_child 5 1471.7 77268 3022.2
## + gender:is_first_child 1 57.0 75739 3022.4
## - parent_educ:parent_marital_status 15 4190.6 79986 3022.6
## + gender:lunch_type 1 8.1 75788 3022.8
## + gender:practice_sport 2 232.2 75564 3023.0
## + is_first_child:wkly_study_hours 2 230.4 75565 3023.1
## + gender:wkly_study_hours 2 198.3 75598 3023.3
## - ethnic_group:transport_means 4 1355.1 77151 3023.3
## + transport_means:wkly_study_hours 2 165.8 75630 3023.6
## + practice_sport:transport_means 2 91.4 75704 3024.1
## + practice_sport:is_first_child 2 30.8 75765 3024.6
## + ethnic_group:lunch_type 4 528.1 75268 3024.7
## + ethnic_group:test_prep 4 488.7 75307 3025.0
## + test_prep:parent_marital_status 3 207.7 75588 3025.2
## + lunch_type:parent_marital_status 3 150.2 75646 3025.7
## + parent_educ:practice_sport 10 1908.4 73887 3025.8
## + ethnic_group:is_first_child 4 370.0 75426 3026.0
## + gender:parent_marital_status 3 58.6 75737 3026.4
## + parent_educ:transport_means 5 568.5 75227 3026.4
## - parent_marital_status:wkly_study_hours 6 2312.6 78108 3026.6
## + gender:ethnic_group 4 219.5 75576 3027.1
## + parent_educ:lunch_type 5 453.2 75343 3027.3
## + gender:parent_educ 5 447.8 75348 3027.3
## - lunch_type:practice_sport 2 1433.9 77230 3027.9
## + ethnic_group:practice_sport 8 1075.1 74721 3028.4
## + parent_marital_status:practice_sport 6 536.8 75259 3028.7
## + parent_educ:wkly_study_hours 10 1464.0 74332 3029.3
## + parent_educ:test_prep 5 129.7 75666 3029.8
## - parent_marital_status:is_first_child 3 2041.9 77838 3030.5
## + ethnic_group:parent_marital_status 11 1532.8 74263 3030.8
## + ethnic_group:wkly_study_hours 8 698.7 75097 3031.4
## + ethnic_group:parent_educ 20 2190.8 73605 3043.5
##
## Step: AIC=3019.34
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:transport_means +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 61.1 75920 3017.8
## - test_prep:is_first_child 1 66.6 75926 3017.9
## - is_first_child:transport_means 1 121.1 75980 3018.3
## - test_prep:transport_means 1 123.3 75982 3018.3
## - practice_sport:wkly_study_hours 4 907.1 76766 3018.3
## - test_prep:practice_sport 2 408.5 76267 3018.5
## - lunch_type:is_first_child 1 162.8 76022 3018.6
## - test_prep:wkly_study_hours 2 472.7 76332 3019.0
## - lunch_type:test_prep 1 249.1 76108 3019.3
## <none> 75859 3019.3
## - lunch_type:wkly_study_hours 2 582.1 76441 3019.8
## - parent_marital_status:transport_means 3 852.8 76712 3019.9
## - lunch_type:transport_means 1 379.7 76239 3020.3
## - parent_educ:is_first_child 5 1449.5 77308 3020.5
## - parent_educ:parent_marital_status 15 4159.3 80018 3020.8
## + gender:test_prep 1 63.1 75796 3020.8
## + gender:is_first_child 1 51.0 75808 3020.9
## + gender:lunch_type 1 5.8 75853 3021.3
## + gender:practice_sport 2 246.4 75613 3021.4
## + is_first_child:wkly_study_hours 2 231.2 75628 3021.5
## + gender:wkly_study_hours 2 218.9 75640 3021.6
## - ethnic_group:transport_means 4 1372.6 77232 3021.9
## + transport_means:wkly_study_hours 2 153.6 75705 3022.1
## + practice_sport:transport_means 2 88.4 75771 3022.7
## + practice_sport:is_first_child 2 33.0 75826 3023.1
## + ethnic_group:lunch_type 4 538.8 75320 3023.1
## + ethnic_group:test_prep 4 464.8 75394 3023.7
## + test_prep:parent_marital_status 3 205.5 75653 3023.7
## + lunch_type:parent_marital_status 3 157.5 75702 3024.1
## + parent_educ:practice_sport 10 1925.9 73933 3024.2
## + ethnic_group:is_first_child 4 351.2 75508 3024.6
## - parent_marital_status:wkly_study_hours 6 2281.3 78140 3024.8
## + gender:parent_marital_status 3 61.3 75798 3024.9
## + parent_educ:transport_means 5 558.7 75300 3025.0
## + gender:ethnic_group 4 231.9 75627 3025.5
## + gender:parent_educ 5 446.9 75412 3025.8
## + parent_educ:lunch_type 5 444.2 75415 3025.9
## - lunch_type:practice_sport 2 1417.7 77277 3026.3
## + parent_marital_status:practice_sport 6 550.5 75308 3027.0
## + ethnic_group:practice_sport 8 1054.5 74804 3027.1
## + parent_educ:wkly_study_hours 10 1478.9 74380 3027.7
## + parent_educ:test_prep 5 132.2 75727 3028.3
## - parent_marital_status:is_first_child 3 2002.0 77861 3028.7
## + ethnic_group:parent_marital_status 11 1567.5 74291 3029.0
## + ethnic_group:wkly_study_hours 8 725.0 75134 3029.7
## + ethnic_group:parent_educ 20 2197.5 73662 3042.0
##
## Step: AIC=3017.81
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - test_prep:is_first_child 1 71.6 75992 3016.4
## - practice_sport:wkly_study_hours 4 888.2 76808 3016.7
## - is_first_child:transport_means 1 131.9 76052 3016.8
## - test_prep:transport_means 1 138.8 76059 3016.9
## - test_prep:practice_sport 2 403.4 76323 3016.9
## - lunch_type:is_first_child 1 150.7 76071 3017.0
## - test_prep:wkly_study_hours 2 477.5 76397 3017.5
## - lunch_type:test_prep 1 253.8 76174 3017.8
## <none> 75920 3017.8
## - lunch_type:wkly_study_hours 2 565.9 76486 3018.2
## - parent_marital_status:transport_means 3 851.0 76771 3018.4
## - parent_educ:is_first_child 5 1432.0 77352 3018.8
## - lunch_type:transport_means 1 393.6 76314 3018.9
## - parent_educ:parent_marital_status 15 4127.3 80047 3019.1
## + gender:transport_means 1 61.1 75859 3019.3
## + gender:test_prep 1 52.4 75868 3019.4
## + gender:is_first_child 1 50.5 75870 3019.4
## + gender:lunch_type 1 7.1 75913 3019.8
## + gender:practice_sport 2 255.3 75665 3019.8
## + is_first_child:wkly_study_hours 2 236.9 75683 3020.0
## + gender:wkly_study_hours 2 221.6 75698 3020.1
## - ethnic_group:transport_means 4 1335.2 77255 3020.1
## + transport_means:wkly_study_hours 2 154.0 75766 3020.6
## + practice_sport:transport_means 2 89.3 75831 3021.1
## + practice_sport:is_first_child 2 37.7 75882 3021.5
## + ethnic_group:lunch_type 4 532.3 75388 3021.7
## + ethnic_group:test_prep 4 467.3 75453 3022.2
## + test_prep:parent_marital_status 3 200.6 75719 3022.2
## + parent_educ:practice_sport 10 1954.7 73965 3022.4
## + lunch_type:parent_marital_status 3 160.5 75760 3022.6
## + ethnic_group:is_first_child 4 355.2 75565 3023.1
## - parent_marital_status:wkly_study_hours 6 2270.6 78191 3023.2
## + gender:parent_marital_status 3 59.3 75861 3023.3
## + parent_educ:transport_means 5 560.2 75360 3023.4
## + gender:ethnic_group 4 247.9 75672 3023.9
## + gender:parent_educ 5 449.9 75470 3024.3
## + parent_educ:lunch_type 5 448.9 75471 3024.3
## - lunch_type:practice_sport 2 1396.7 77317 3024.6
## + parent_marital_status:practice_sport 6 550.3 75370 3025.5
## + ethnic_group:practice_sport 8 1036.1 74884 3025.7
## + parent_educ:wkly_study_hours 10 1435.0 74485 3026.6
## + parent_educ:test_prep 5 128.0 75792 3026.8
## + ethnic_group:parent_marital_status 11 1602.7 74317 3027.2
## - parent_marital_status:is_first_child 3 2036.3 77956 3027.4
## + ethnic_group:wkly_study_hours 8 718.1 75202 3028.2
## + ethnic_group:parent_educ 20 2173.1 73747 3040.7
## - gender 1 12750.1 88670 3107.4
##
## Step: AIC=3016.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 915.5 76907 3015.4
## - is_first_child:transport_means 1 140.3 76132 3015.5
## - test_prep:transport_means 1 140.4 76132 3015.5
## - test_prep:practice_sport 2 403.2 76395 3015.5
## - lunch_type:is_first_child 1 166.0 76158 3015.7
## - test_prep:wkly_study_hours 2 471.7 76463 3016.0
## - lunch_type:test_prep 1 244.8 76236 3016.3
## <none> 75992 3016.4
## - parent_marital_status:transport_means 3 837.7 76829 3016.8
## - lunch_type:wkly_study_hours 2 582.5 76574 3016.9
## - parent_educ:is_first_child 5 1386.8 77378 3017.0
## - parent_educ:parent_marital_status 15 4132.9 80125 3017.6
## - lunch_type:transport_means 1 429.9 76421 3017.7
## + test_prep:is_first_child 1 71.6 75920 3017.8
## + gender:transport_means 1 66.1 75926 3017.9
## + gender:is_first_child 1 59.1 75933 3017.9
## + gender:test_prep 1 52.7 75939 3018.0
## + gender:lunch_type 1 8.3 75983 3018.3
## + gender:practice_sport 2 244.1 75748 3018.5
## + gender:wkly_study_hours 2 240.2 75751 3018.5
## - ethnic_group:transport_means 4 1326.3 77318 3018.6
## + is_first_child:wkly_study_hours 2 213.2 75778 3018.7
## + transport_means:wkly_study_hours 2 158.8 75833 3019.1
## + practice_sport:transport_means 2 91.2 75900 3019.7
## + practice_sport:is_first_child 2 28.3 75963 3020.2
## + ethnic_group:lunch_type 4 528.2 75463 3020.3
## + test_prep:parent_marital_status 3 219.9 75772 3020.7
## + ethnic_group:test_prep 4 467.8 75524 3020.7
## + parent_educ:practice_sport 10 1968.3 74023 3020.9
## + lunch_type:parent_marital_status 3 163.3 75828 3021.1
## + ethnic_group:is_first_child 4 365.5 75626 3021.5
## - parent_marital_status:wkly_study_hours 6 2263.7 78255 3021.7
## + parent_educ:transport_means 5 583.3 75408 3021.8
## + gender:parent_marital_status 3 64.3 75927 3021.9
## + gender:ethnic_group 4 233.9 75758 3022.6
## + gender:parent_educ 5 453.0 75539 3022.8
## + parent_educ:lunch_type 5 439.7 75552 3022.9
## - lunch_type:practice_sport 2 1447.7 77439 3023.5
## + parent_marital_status:practice_sport 6 544.3 75447 3024.1
## + ethnic_group:practice_sport 8 1040.0 74952 3024.2
## + parent_educ:wkly_study_hours 10 1447.2 74544 3025.0
## + parent_educ:test_prep 5 136.2 75855 3025.3
## - parent_marital_status:is_first_child 3 1998.8 77990 3025.7
## + ethnic_group:parent_marital_status 11 1600.7 74391 3025.8
## + ethnic_group:wkly_study_hours 8 727.9 75264 3026.7
## + ethnic_group:parent_educ 20 2203.3 73788 3039.0
## - gender 1 12874.8 88866 3106.7
##
## Step: AIC=3015.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - lunch_type:is_first_child 1 112.2 77019 3014.3
## - is_first_child:transport_means 1 131.0 77038 3014.4
## - test_prep:transport_means 1 140.5 77048 3014.5
## - parent_educ:is_first_child 5 1213.8 78121 3014.7
## - test_prep:practice_sport 2 447.6 77355 3014.9
## <none> 76907 3015.4
## - test_prep:wkly_study_hours 2 530.7 77438 3015.5
## - lunch_type:wkly_study_hours 2 537.6 77445 3015.6
## - lunch_type:test_prep 1 292.2 77199 3015.7
## - parent_marital_status:transport_means 3 855.9 77763 3016.0
## - parent_educ:parent_marital_status 15 4099.1 81006 3016.1
## - lunch_type:transport_means 1 378.0 77285 3016.3
## + practice_sport:wkly_study_hours 4 915.5 75992 3016.4
## + test_prep:is_first_child 1 98.9 76808 3016.7
## + gender:is_first_child 1 98.6 76808 3016.7
## - ethnic_group:transport_means 4 1240.6 78148 3016.9
## + gender:practice_sport 2 316.3 76591 3017.0
## + gender:transport_means 1 46.6 76860 3017.1
## + gender:test_prep 1 42.4 76865 3017.1
## + is_first_child:wkly_study_hours 2 284.8 76622 3017.2
## + gender:lunch_type 1 6.1 76901 3017.4
## + gender:wkly_study_hours 2 223.6 76683 3017.7
## + transport_means:wkly_study_hours 2 181.5 76726 3018.0
## + practice_sport:transport_means 2 74.7 76832 3018.9
## + practice_sport:is_first_child 2 50.1 76857 3019.1
## + ethnic_group:test_prep 4 485.1 76422 3019.7
## + test_prep:parent_marital_status 3 175.0 76732 3020.1
## + ethnic_group:lunch_type 4 427.3 76480 3020.2
## + parent_educ:transport_means 5 659.0 76248 3020.4
## + ethnic_group:is_first_child 4 398.8 76508 3020.4
## + lunch_type:parent_marital_status 3 136.8 76770 3020.4
## + gender:parent_marital_status 3 70.3 76837 3020.9
## + parent_educ:practice_sport 10 1831.0 75076 3021.2
## + parent_educ:lunch_type 5 538.8 76368 3021.3
## - parent_marital_status:wkly_study_hours 6 2382.5 79290 3021.4
## + gender:parent_educ 5 483.0 76424 3021.7
## + gender:ethnic_group 4 222.0 76685 3021.7
## - lunch_type:practice_sport 2 1420.3 78327 3022.2
## + parent_marital_status:practice_sport 6 507.1 76400 3023.5
## + ethnic_group:practice_sport 8 971.4 75936 3023.9
## - parent_marital_status:is_first_child 3 1939.7 78847 3024.1
## + parent_educ:test_prep 5 141.9 76765 3024.3
## + parent_educ:wkly_study_hours 10 1326.1 75581 3025.2
## + ethnic_group:wkly_study_hours 8 766.2 76141 3025.5
## + ethnic_group:parent_marital_status 11 1519.3 75388 3025.7
## + ethnic_group:parent_educ 20 2096.4 74811 3039.1
## - gender 1 12541.2 89448 3102.6
##
## Step: AIC=3014.3
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - test_prep:transport_means 1 124.8 77144 3013.2
## - is_first_child:transport_means 1 128.6 77148 3013.3
## - parent_educ:is_first_child 5 1211.9 78231 3013.5
## - test_prep:practice_sport 2 461.2 77481 3013.8
## - test_prep:wkly_study_hours 2 519.7 77539 3014.3
## <none> 77019 3014.3
## - lunch_type:wkly_study_hours 2 554.4 77574 3014.5
## - lunch_type:test_prep 1 300.8 77320 3014.6
## - parent_marital_status:transport_means 3 840.4 77860 3014.7
## - lunch_type:transport_means 1 363.1 77382 3015.1
## - parent_educ:parent_marital_status 15 4150.6 81170 3015.3
## + lunch_type:is_first_child 1 112.2 76907 3015.4
## + test_prep:is_first_child 1 111.9 76907 3015.4
## + gender:is_first_child 1 87.1 76932 3015.6
## + practice_sport:wkly_study_hours 4 861.7 76158 3015.7
## + gender:practice_sport 2 343.3 76676 3015.7
## - ethnic_group:transport_means 4 1239.7 78259 3015.7
## + is_first_child:wkly_study_hours 2 316.6 76703 3015.9
## + gender:transport_means 1 38.4 76981 3016.0
## + gender:test_prep 1 38.3 76981 3016.0
## + gender:lunch_type 1 7.9 77011 3016.2
## + gender:wkly_study_hours 2 220.2 76799 3016.6
## + transport_means:wkly_study_hours 2 189.0 76830 3016.8
## + practice_sport:transport_means 2 81.6 76938 3017.7
## + practice_sport:is_first_child 2 54.8 76965 3017.9
## + ethnic_group:test_prep 4 488.8 76530 3018.5
## + ethnic_group:is_first_child 4 441.0 76578 3018.9
## + test_prep:parent_marital_status 3 175.7 76844 3018.9
## + ethnic_group:lunch_type 4 416.5 76603 3019.1
## + lunch_type:parent_marital_status 3 133.8 76886 3019.3
## + parent_educ:transport_means 5 649.1 76370 3019.3
## + gender:parent_marital_status 3 64.9 76954 3019.8
## + parent_educ:practice_sport 10 1810.2 75209 3020.3
## + parent_educ:lunch_type 5 522.4 76497 3020.3
## + gender:ethnic_group 4 235.2 76784 3020.5
## + gender:parent_educ 5 491.0 76528 3020.5
## - parent_marital_status:wkly_study_hours 6 2433.8 79453 3020.7
## - lunch_type:practice_sport 2 1430.6 78450 3021.2
## + ethnic_group:practice_sport 8 970.5 76049 3022.8
## + parent_marital_status:practice_sport 6 428.5 76591 3023.0
## + parent_educ:test_prep 5 143.4 76876 3023.2
## - parent_marital_status:is_first_child 3 2057.4 79077 3023.8
## + parent_educ:wkly_study_hours 10 1304.5 75715 3024.2
## + ethnic_group:wkly_study_hours 8 774.1 76245 3024.3
## + ethnic_group:parent_marital_status 11 1464.4 75555 3025.0
## + ethnic_group:parent_educ 20 2101.3 74918 3038.0
## - gender 1 12517.3 89537 3101.2
##
## Step: AIC=3013.25
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - is_first_child:transport_means 1 144.1 77288 3012.3
## - parent_educ:is_first_child 5 1232.2 78376 3012.6
## - test_prep:practice_sport 2 465.7 77610 3012.8
## - lunch_type:wkly_study_hours 2 493.4 77638 3013.0
## - test_prep:wkly_study_hours 2 504.4 77648 3013.1
## <none> 77144 3013.2
## - lunch_type:test_prep 1 306.8 77451 3013.6
## - parent_marital_status:transport_means 3 855.0 77999 3013.8
## - lunch_type:transport_means 1 345.9 77490 3013.9
## + test_prep:transport_means 1 124.8 77019 3014.3
## + test_prep:is_first_child 1 112.4 77032 3014.4
## + lunch_type:is_first_child 1 96.5 77048 3014.5
## + gender:is_first_child 1 90.9 77053 3014.6
## + practice_sport:wkly_study_hours 4 867.3 76277 3014.6
## + is_first_child:wkly_study_hours 2 335.0 76809 3014.7
## + gender:practice_sport 2 333.9 76810 3014.7
## - parent_educ:parent_marital_status 15 4230.9 81375 3014.8
## + gender:transport_means 1 51.1 77093 3014.9
## + gender:test_prep 1 33.7 77110 3015.0
## - ethnic_group:transport_means 4 1302.9 78447 3015.1
## + gender:lunch_type 1 11.5 77133 3015.2
## + gender:wkly_study_hours 2 229.6 76915 3015.5
## + transport_means:wkly_study_hours 2 164.7 76979 3016.0
## + practice_sport:transport_means 2 74.8 77069 3016.7
## + practice_sport:is_first_child 2 51.2 77093 3016.9
## + ethnic_group:test_prep 4 518.1 76626 3017.3
## + test_prep:parent_marital_status 3 193.8 76950 3017.8
## + ethnic_group:lunch_type 4 426.6 76718 3018.0
## + parent_educ:transport_means 5 682.3 76462 3018.0
## + ethnic_group:is_first_child 4 417.4 76727 3018.1
## + lunch_type:parent_marital_status 3 140.0 77004 3018.2
## + gender:parent_marital_status 3 62.0 77082 3018.8
## + parent_educ:lunch_type 5 527.7 76616 3019.2
## + parent_educ:practice_sport 10 1795.9 75348 3019.3
## + gender:ethnic_group 4 244.1 76900 3019.4
## + gender:parent_educ 5 499.9 76644 3019.4
## - parent_marital_status:wkly_study_hours 6 2412.6 79557 3019.4
## - lunch_type:practice_sport 2 1455.1 78599 3020.3
## + ethnic_group:practice_sport 8 984.2 76160 3021.7
## + parent_marital_status:practice_sport 6 418.9 76725 3022.0
## + parent_educ:test_prep 5 144.9 76999 3022.1
## - parent_marital_status:is_first_child 3 2069.6 79214 3022.9
## + parent_educ:wkly_study_hours 10 1307.3 75837 3023.2
## + ethnic_group:wkly_study_hours 8 770.1 76374 3023.3
## + ethnic_group:parent_marital_status 11 1459.7 75684 3024.0
## + ethnic_group:parent_educ 20 2023.1 75121 3037.6
## - gender 1 12401.3 89545 3099.2
##
## Step: AIC=3012.35
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 469.3 77757 3011.9
## - parent_educ:is_first_child 5 1272.3 78560 3012.0
## - test_prep:wkly_study_hours 2 508.1 77796 3012.2
## - lunch_type:wkly_study_hours 2 524.0 77812 3012.3
## <none> 77288 3012.3
## - lunch_type:test_prep 1 272.9 77561 3012.4
## - lunch_type:transport_means 1 336.5 77625 3012.9
## + is_first_child:transport_means 1 144.1 77144 3013.2
## + test_prep:transport_means 1 140.3 77148 3013.3
## + test_prep:is_first_child 1 122.9 77165 3013.4
## + lunch_type:is_first_child 1 93.2 77195 3013.6
## + gender:practice_sport 2 346.5 76942 3013.7
## - parent_marital_status:transport_means 3 971.0 78259 3013.7
## + gender:is_first_child 1 78.7 77209 3013.8
## + practice_sport:wkly_study_hours 4 859.2 76429 3013.8
## - parent_educ:parent_marital_status 15 4238.5 81527 3013.8
## + gender:transport_means 1 62.3 77226 3013.9
## + is_first_child:wkly_study_hours 2 301.1 76987 3014.1
## + gender:test_prep 1 30.1 77258 3014.1
## + gender:lunch_type 1 8.4 77280 3014.3
## - ethnic_group:transport_means 4 1313.4 78602 3014.3
## + gender:wkly_study_hours 2 218.6 77070 3014.7
## + transport_means:wkly_study_hours 2 163.3 77125 3015.1
## + practice_sport:transport_means 2 89.4 77199 3015.7
## + practice_sport:is_first_child 2 64.9 77223 3015.9
## + ethnic_group:test_prep 4 542.2 76746 3016.2
## + test_prep:parent_marital_status 3 183.1 77105 3016.9
## + ethnic_group:lunch_type 4 413.2 76875 3017.2
## + lunch_type:parent_marital_status 3 139.1 77149 3017.3
## + parent_educ:transport_means 5 635.8 76652 3017.5
## + gender:parent_marital_status 3 80.3 77208 3017.7
## + ethnic_group:is_first_child 4 330.6 76958 3017.8
## + parent_educ:lunch_type 5 529.8 76758 3018.3
## + gender:ethnic_group 4 247.6 77041 3018.5
## + gender:parent_educ 5 496.8 76791 3018.6
## - parent_marital_status:wkly_study_hours 6 2429.0 79717 3018.6
## + parent_educ:practice_sport 10 1711.9 75576 3019.1
## - lunch_type:practice_sport 2 1445.6 78734 3019.3
## + ethnic_group:practice_sport 8 1012.9 76275 3020.6
## + parent_educ:test_prep 5 179.0 77109 3021.0
## + parent_marital_status:practice_sport 6 437.9 76850 3021.0
## - parent_marital_status:is_first_child 3 2038.1 79326 3021.7
## + parent_educ:wkly_study_hours 10 1301.9 75986 3022.3
## + ethnic_group:wkly_study_hours 8 781.1 76507 3022.4
## + ethnic_group:parent_marital_status 11 1531.4 75757 3022.6
## + ethnic_group:parent_educ 20 1990.8 75297 3037.0
## - gender 1 12297.8 89586 3097.5
##
## Step: AIC=3011.92
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:wkly_study_hours 2 503.4 78261 3011.7
## <none> 77757 3011.9
## - lunch_type:test_prep 1 290.1 78048 3012.1
## - lunch_type:transport_means 1 318.4 78076 3012.3
## + test_prep:practice_sport 2 469.3 77288 3012.3
## - lunch_type:wkly_study_hours 2 588.6 78346 3012.4
## - parent_educ:parent_marital_status 15 4157.8 81915 3012.7
## + is_first_child:transport_means 1 147.6 77610 3012.8
## + test_prep:transport_means 1 145.3 77612 3012.8
## + test_prep:is_first_child 1 122.2 77635 3013.0
## + gender:practice_sport 2 383.7 77374 3013.0
## - parent_educ:is_first_child 5 1477.9 79235 3013.0
## - parent_marital_status:transport_means 3 950.8 78708 3013.1
## + lunch_type:is_first_child 1 106.0 77652 3013.1
## + practice_sport:wkly_study_hours 4 891.5 76866 3013.1
## - ethnic_group:transport_means 4 1242.4 79000 3013.3
## + gender:is_first_child 1 59.5 77698 3013.5
## + gender:transport_means 1 54.2 77703 3013.5
## + gender:test_prep 1 25.3 77732 3013.7
## + gender:lunch_type 1 15.2 77742 3013.8
## + is_first_child:wkly_study_hours 2 265.7 77492 3013.9
## + transport_means:wkly_study_hours 2 199.8 77558 3014.4
## + gender:wkly_study_hours 2 198.7 77559 3014.4
## + practice_sport:is_first_child 2 85.8 77672 3015.3
## + practice_sport:transport_means 2 82.6 77675 3015.3
## + test_prep:parent_marital_status 3 234.8 77523 3016.1
## + ethnic_group:lunch_type 4 460.3 77297 3016.4
## + ethnic_group:test_prep 4 451.0 77306 3016.5
## + lunch_type:parent_marital_status 3 142.6 77615 3016.8
## + parent_educ:transport_means 5 666.7 77091 3016.8
## + gender:parent_marital_status 3 101.5 77656 3017.2
## + ethnic_group:is_first_child 4 337.2 77420 3017.4
## - parent_marital_status:wkly_study_hours 6 2359.6 80117 3017.6
## + parent_educ:lunch_type 5 553.5 77204 3017.7
## + gender:parent_educ 5 531.7 77226 3017.9
## + gender:ethnic_group 4 217.0 77540 3018.3
## + parent_educ:practice_sport 10 1673.0 76084 3019.1
## - lunch_type:practice_sport 2 1545.1 79303 3019.5
## - parent_marital_status:is_first_child 3 1928.4 79686 3020.4
## + ethnic_group:practice_sport 8 981.3 76776 3020.4
## + parent_marital_status:practice_sport 6 444.5 77313 3020.5
## + parent_educ:test_prep 5 146.8 77611 3020.8
## + parent_educ:wkly_study_hours 10 1371.1 76386 3021.4
## + ethnic_group:wkly_study_hours 8 769.9 76988 3022.1
## + ethnic_group:parent_marital_status 11 1497.6 76260 3022.4
## + ethnic_group:parent_educ 20 2102.3 75655 3035.8
## - gender 1 12364.6 90122 3097.0
##
## Step: AIC=3011.73
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:transport_means 1 221.7 78483 3011.4
## <none> 78261 3011.7
## + test_prep:wkly_study_hours 2 503.4 77757 3011.9
## - parent_educ:parent_marital_status 15 4125.9 82387 3012.0
## - lunch_type:test_prep 1 312.1 78573 3012.1
## + test_prep:practice_sport 2 464.6 77796 3012.2
## - ethnic_group:transport_means 4 1170.1 79431 3012.5
## + practice_sport:wkly_study_hours 4 942.3 77319 3012.6
## + is_first_child:transport_means 1 151.9 78109 3012.6
## - lunch_type:wkly_study_hours 2 649.4 78910 3012.6
## + test_prep:transport_means 1 129.4 78132 3012.8
## + test_prep:is_first_child 1 116.8 78144 3012.8
## - parent_marital_status:transport_means 3 952.4 79213 3012.9
## - parent_educ:is_first_child 5 1493.3 79754 3012.9
## + gender:practice_sport 2 370.4 77890 3012.9
## + lunch_type:is_first_child 1 98.9 78162 3013.0
## + gender:transport_means 1 60.3 78201 3013.3
## + gender:is_first_child 1 51.3 78210 3013.3
## + gender:lunch_type 1 22.1 78239 3013.6
## + gender:test_prep 1 14.9 78246 3013.6
## + is_first_child:wkly_study_hours 2 273.1 77988 3013.7
## + gender:wkly_study_hours 2 195.1 78066 3014.3
## + transport_means:wkly_study_hours 2 185.5 78075 3014.3
## + practice_sport:transport_means 2 85.5 78175 3015.1
## + practice_sport:is_first_child 2 56.2 78205 3015.3
## + ethnic_group:test_prep 4 507.3 77754 3015.9
## + test_prep:parent_marital_status 3 218.3 78043 3016.1
## + ethnic_group:lunch_type 4 477.5 77783 3016.1
## + parent_educ:transport_means 5 668.9 77592 3016.7
## + lunch_type:parent_marital_status 3 124.1 78137 3016.8
## + gender:parent_marital_status 3 110.8 78150 3016.9
## - parent_marital_status:wkly_study_hours 6 2347.2 80608 3017.2
## + gender:parent_educ 5 531.0 77730 3017.7
## + parent_educ:lunch_type 5 527.0 77734 3017.8
## + gender:ethnic_group 4 259.9 78001 3017.8
## + ethnic_group:is_first_child 4 236.4 78024 3017.9
## - lunch_type:practice_sport 2 1430.9 79692 3018.4
## + parent_marital_status:practice_sport 6 469.5 77791 3020.2
## + parent_educ:practice_sport 10 1509.6 76751 3020.2
## + parent_educ:test_prep 5 187.2 78074 3020.3
## + parent_educ:wkly_study_hours 10 1467.4 76794 3020.6
## - parent_marital_status:is_first_child 3 2024.8 80286 3020.8
## + ethnic_group:practice_sport 8 898.6 77362 3020.9
## + ethnic_group:parent_marital_status 11 1610.1 76651 3021.5
## + ethnic_group:wkly_study_hours 8 778.1 77483 3021.8
## + ethnic_group:parent_educ 20 2152.2 76109 3035.3
## - gender 1 12415.3 90676 3096.6
##
## Step: AIC=3011.4
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 262.1 78745 3011.4
## <none> 78483 3011.4
## - parent_educ:parent_marital_status 15 4130.4 82613 3011.7
## + lunch_type:transport_means 1 221.7 78261 3011.7
## + test_prep:practice_sport 2 449.9 78033 3012.0
## - ethnic_group:transport_means 4 1161.5 79644 3012.1
## - lunch_type:wkly_study_hours 2 628.3 79111 3012.1
## - parent_educ:is_first_child 5 1457.2 79940 3012.2
## + test_prep:is_first_child 1 146.9 78336 3012.3
## + is_first_child:transport_means 1 144.0 78339 3012.3
## + test_prep:wkly_study_hours 2 406.7 78076 3012.3
## + gender:practice_sport 2 390.3 78092 3012.5
## + test_prep:transport_means 1 116.1 78367 3012.5
## - parent_marital_status:transport_means 3 954.6 79437 3012.5
## + practice_sport:wkly_study_hours 4 897.3 77585 3012.6
## + lunch_type:is_first_child 1 89.8 78393 3012.7
## + gender:transport_means 1 71.0 78412 3012.9
## + gender:is_first_child 1 67.6 78415 3012.9
## + gender:lunch_type 1 31.1 78451 3013.2
## + gender:test_prep 1 21.5 78461 3013.2
## + is_first_child:wkly_study_hours 2 272.3 78210 3013.3
## + gender:wkly_study_hours 2 197.2 78285 3013.9
## + transport_means:wkly_study_hours 2 171.9 78311 3014.1
## + practice_sport:transport_means 2 92.0 78391 3014.7
## + practice_sport:is_first_child 2 53.0 78430 3015.0
## + ethnic_group:lunch_type 4 533.7 77949 3015.4
## + ethnic_group:test_prep 4 514.6 77968 3015.5
## + test_prep:parent_marital_status 3 224.0 78259 3015.7
## + gender:parent_marital_status 3 140.6 78342 3016.3
## + parent_educ:transport_means 5 664.5 77818 3016.4
## + lunch_type:parent_marital_status 3 128.4 78354 3016.4
## + gender:parent_educ 5 587.5 77895 3017.0
## - parent_marital_status:wkly_study_hours 6 2395.3 80878 3017.1
## + parent_educ:lunch_type 5 559.6 77923 3017.2
## + gender:ethnic_group 4 256.9 78226 3017.5
## + ethnic_group:is_first_child 4 221.7 78261 3017.7
## - lunch_type:practice_sport 2 1393.9 79876 3017.8
## + parent_marital_status:practice_sport 6 467.3 78015 3019.9
## + parent_educ:test_prep 5 194.3 78288 3019.9
## + parent_educ:practice_sport 10 1487.5 76995 3020.1
## + parent_educ:wkly_study_hours 10 1441.2 77041 3020.5
## - parent_marital_status:is_first_child 3 2065.7 80548 3020.7
## + ethnic_group:parent_marital_status 11 1648.0 76835 3020.9
## + ethnic_group:practice_sport 8 846.7 77636 3021.0
## + ethnic_group:wkly_study_hours 8 744.7 77738 3021.8
## + ethnic_group:parent_educ 20 2158.3 76324 3034.9
## - gender 1 12321.2 90804 3095.4
##
## Step: AIC=3011.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:parent_marital_status 15 4063.4 82808 3011.1
## <none> 78745 3011.4
## + lunch_type:test_prep 1 262.1 78483 3011.4
## - lunch_type:wkly_study_hours 2 575.8 79321 3011.7
## + test_prep:practice_sport 2 468.3 78276 3011.8
## - parent_educ:is_first_child 5 1428.4 80173 3012.0
## - ethnic_group:transport_means 4 1168.4 79913 3012.1
## + lunch_type:transport_means 1 171.7 78573 3012.1
## + test_prep:wkly_study_hours 2 435.1 78310 3012.1
## + practice_sport:wkly_study_hours 4 949.3 77795 3012.2
## - parent_marital_status:transport_means 3 939.6 79684 3012.4
## + test_prep:is_first_child 1 129.3 78615 3012.4
## + test_prep:transport_means 1 121.3 78623 3012.5
## + gender:practice_sport 2 386.6 78358 3012.5
## + is_first_child:transport_means 1 112.6 78632 3012.5
## + lunch_type:is_first_child 1 100.4 78644 3012.6
## + gender:is_first_child 1 76.3 78668 3012.8
## + gender:transport_means 1 74.0 78671 3012.8
## + gender:lunch_type 1 46.0 78699 3013.0
## + is_first_child:wkly_study_hours 2 312.2 78432 3013.0
## + gender:test_prep 1 29.1 78716 3013.2
## + gender:wkly_study_hours 2 197.1 78548 3013.9
## + transport_means:wkly_study_hours 2 173.8 78571 3014.1
## + practice_sport:transport_means 2 114.1 78631 3014.5
## + practice_sport:is_first_child 2 62.2 78683 3014.9
## + ethnic_group:lunch_type 4 561.7 78183 3015.1
## + ethnic_group:test_prep 4 525.1 78220 3015.4
## + test_prep:parent_marital_status 3 228.3 78516 3015.7
## + parent_educ:transport_means 5 680.5 78064 3016.2
## + gender:parent_marital_status 3 140.2 78604 3016.3
## + lunch_type:parent_marital_status 3 119.1 78626 3016.5
## + gender:parent_educ 5 618.2 78126 3016.7
## + parent_educ:lunch_type 5 559.3 78185 3017.2
## - parent_marital_status:wkly_study_hours 6 2417.6 81162 3017.2
## + gender:ethnic_group 4 269.6 78475 3017.3
## + ethnic_group:is_first_child 4 245.7 78499 3017.5
## - lunch_type:practice_sport 2 1369.3 80114 3017.5
## + parent_educ:practice_sport 10 1524.1 77221 3019.8
## + parent_educ:wkly_study_hours 10 1522.8 77222 3019.8
## + parent_marital_status:practice_sport 6 467.4 78277 3019.9
## + parent_educ:test_prep 5 186.3 78558 3020.0
## + ethnic_group:practice_sport 8 913.7 77831 3020.5
## - parent_marital_status:is_first_child 3 2115.1 80860 3021.0
## + ethnic_group:wkly_study_hours 8 829.7 77915 3021.1
## + ethnic_group:parent_marital_status 11 1564.4 77180 3021.5
## + ethnic_group:parent_educ 20 2215.7 76529 3034.5
## - test_prep 1 9863.4 88608 3079.0
## - gender 1 12254.8 91000 3094.7
##
## Step: AIC=3011.05
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:is_first_child + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:transport_means 3 657.5 83466 3009.7
## - parent_educ:is_first_child 5 1407.4 84216 3011.0
## <none> 82808 3011.1
## + parent_educ:parent_marital_status 15 4063.4 78745 3011.4
## + test_prep:transport_means 1 195.2 82613 3011.7
## + lunch_type:test_prep 1 195.1 82613 3011.7
## + gender:practice_sport 2 473.7 82334 3011.7
## + lunch_type:transport_means 1 185.2 82623 3011.7
## - ethnic_group:transport_means 4 1252.3 84060 3011.9
## + lunch_type:is_first_child 1 148.1 82660 3012.0
## + is_first_child:transport_means 1 126.7 82681 3012.2
## + test_prep:is_first_child 1 126.1 82682 3012.2
## + test_prep:wkly_study_hours 2 396.1 82412 3012.2
## - lunch_type:wkly_study_hours 2 731.3 83539 3012.2
## + test_prep:practice_sport 2 380.1 82428 3012.3
## + gender:is_first_child 1 70.3 82738 3012.6
## + is_first_child:wkly_study_hours 2 345.7 82462 3012.6
## + practice_sport:wkly_study_hours 4 881.8 81926 3012.7
## + gender:transport_means 1 38.6 82770 3012.8
## + gender:lunch_type 1 36.2 82772 3012.8
## + gender:test_prep 1 12.1 82796 3013.0
## + gender:wkly_study_hours 2 277.5 82531 3013.1
## + transport_means:wkly_study_hours 2 155.0 82653 3013.9
## + practice_sport:transport_means 2 76.8 82731 3014.5
## + gender:parent_educ 5 878.7 81929 3014.8
## + practice_sport:is_first_child 2 21.4 82787 3014.9
## - parent_marital_status:wkly_study_hours 6 2271.7 85080 3015.0
## - lunch_type:practice_sport 2 1129.5 83938 3015.1
## + lunch_type:parent_marital_status 3 198.0 82610 3015.6
## + ethnic_group:test_prep 4 455.0 82353 3015.8
## + parent_educ:wkly_study_hours 10 2108.4 80700 3015.8
## - parent_marital_status:is_first_child 3 1546.8 84355 3016.0
## + test_prep:parent_marital_status 3 138.0 82670 3016.1
## + gender:parent_marital_status 3 117.4 82691 3016.2
## + parent_educ:transport_means 5 654.1 82154 3016.4
## + gender:ethnic_group 4 364.0 82444 3016.4
## + ethnic_group:lunch_type 4 347.8 82460 3016.6
## + ethnic_group:is_first_child 4 240.9 82567 3017.3
## + parent_educ:lunch_type 5 513.6 82295 3017.4
## + parent_marital_status:practice_sport 6 744.7 82063 3017.7
## + parent_educ:practice_sport 10 1768.3 81040 3018.3
## + parent_educ:test_prep 5 292.1 82516 3019.0
## + ethnic_group:practice_sport 8 1100.3 81708 3019.2
## + ethnic_group:parent_marital_status 11 1823.4 80985 3019.9
## + ethnic_group:wkly_study_hours 8 839.1 81969 3021.1
## + ethnic_group:parent_educ 20 2212.2 80596 3035.1
## - test_prep 1 9566.9 92375 3073.6
## - gender 1 12656.8 95465 3093.0
##
## Step: AIC=3009.72
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:is_first_child + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:is_first_child 5 1301.6 84767 3008.8
## <none> 83466 3009.7
## - ethnic_group:transport_means 4 1174.0 84640 3010.0
## + test_prep:transport_means 1 229.8 83236 3010.1
## + is_first_child:transport_means 1 215.1 83251 3010.2
## + lunch_type:test_prep 1 186.9 83279 3010.4
## + lunch_type:transport_means 1 186.6 83279 3010.4
## - lunch_type:wkly_study_hours 2 708.4 84174 3010.7
## + lunch_type:is_first_child 1 131.4 83334 3010.8
## + test_prep:is_first_child 1 127.4 83338 3010.8
## + gender:practice_sport 2 407.4 83058 3010.8
## + gender:is_first_child 1 96.5 83369 3011.0
## + parent_marital_status:transport_means 3 657.5 82808 3011.1
## + test_prep:wkly_study_hours 2 375.5 83090 3011.1
## + test_prep:practice_sport 2 375.2 83090 3011.1
## + gender:transport_means 1 31.2 83435 3011.5
## + gender:lunch_type 1 24.1 83442 3011.6
## + gender:test_prep 1 17.3 83448 3011.6
## + practice_sport:wkly_study_hours 4 858.9 82607 3011.6
## + gender:wkly_study_hours 2 280.1 83186 3011.7
## + is_first_child:wkly_study_hours 2 278.3 83187 3011.8
## + parent_educ:parent_marital_status 15 3781.3 79684 3012.4
## - parent_marital_status:wkly_study_hours 6 2151.2 85617 3012.7
## + transport_means:wkly_study_hours 2 134.1 83332 3012.8
## + gender:parent_educ 5 969.9 82496 3012.8
## + practice_sport:transport_means 2 108.4 83357 3012.9
## + practice_sport:is_first_child 2 9.9 83456 3013.7
## + test_prep:parent_marital_status 3 220.3 83245 3014.2
## + parent_educ:wkly_study_hours 10 2160.5 81305 3014.2
## + lunch_type:parent_marital_status 3 191.9 83274 3014.4
## - lunch_type:practice_sport 2 1249.9 84716 3014.5
## + gender:parent_marital_status 3 129.0 83337 3014.8
## + gender:ethnic_group 4 409.1 83057 3014.8
## + ethnic_group:test_prep 4 400.2 83065 3014.9
## - parent_marital_status:is_first_child 3 1618.7 85084 3015.1
## + parent_educ:transport_means 5 613.7 82852 3015.4
## + ethnic_group:lunch_type 4 331.8 83134 3015.4
## + parent_educ:lunch_type 5 499.0 82967 3016.2
## + parent_educ:practice_sport 10 1891.8 81574 3016.2
## + ethnic_group:is_first_child 4 190.0 83276 3016.4
## + parent_marital_status:practice_sport 6 751.8 82714 3016.4
## + ethnic_group:practice_sport 8 1191.8 82274 3017.2
## + parent_educ:test_prep 5 302.8 83163 3017.6
## + ethnic_group:parent_marital_status 11 1930.5 81535 3017.9
## + ethnic_group:wkly_study_hours 8 816.2 82649 3019.9
## + ethnic_group:parent_educ 20 2008.0 81458 3035.3
## - test_prep 1 9947.6 93413 3074.2
## - gender 1 12642.9 96109 3090.9
##
## Step: AIC=3008.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## <none> 84767 3008.8
## + test_prep:transport_means 1 263.6 84504 3009.0
## + test_prep:practice_sport 2 543.3 84224 3009.1
## + is_first_child:transport_means 1 254.5 84513 3009.1
## - ethnic_group:transport_means 4 1232.7 86000 3009.4
## - lunch_type:wkly_study_hours 2 680.0 85447 3009.6
## + lunch_type:test_prep 1 164.4 84603 3009.7
## + parent_educ:is_first_child 5 1301.6 83466 3009.7
## + lunch_type:transport_means 1 139.2 84628 3009.9
## + lunch_type:is_first_child 1 125.4 84642 3010.0
## + gender:practice_sport 2 401.7 84366 3010.1
## + gender:is_first_child 1 108.5 84659 3010.1
## + test_prep:wkly_study_hours 2 383.2 84384 3010.2
## + test_prep:is_first_child 1 63.8 84704 3010.4
## + gender:lunch_type 1 22.9 84744 3010.7
## + gender:transport_means 1 19.0 84748 3010.7
## + gender:test_prep 1 5.3 84762 3010.8
## + parent_marital_status:transport_means 3 551.7 84216 3011.0
## - parent_marital_status:wkly_study_hours 6 2060.3 86828 3011.0
## + gender:wkly_study_hours 2 232.3 84535 3011.2
## + is_first_child:wkly_study_hours 2 193.2 84574 3011.5
## + parent_educ:parent_marital_status 15 3818.8 80949 3011.7
## + transport_means:wkly_study_hours 2 107.3 84660 3012.1
## + practice_sport:transport_means 2 103.2 84664 3012.1
## + practice_sport:wkly_study_hours 4 671.8 84096 3012.2
## - parent_marital_status:is_first_child 3 1395.1 86162 3012.5
## + gender:parent_educ 5 882.7 83885 3012.7
## + practice_sport:is_first_child 2 3.9 84763 3012.8
## + test_prep:parent_marital_status 3 189.7 84578 3013.5
## - lunch_type:practice_sport 2 1258.7 86026 3013.6
## + ethnic_group:test_prep 4 470.3 84297 3013.6
## + lunch_type:parent_marital_status 3 184.0 84583 3013.6
## + gender:ethnic_group 4 464.8 84303 3013.6
## + parent_educ:practice_sport 10 2151.4 82616 3013.7
## + ethnic_group:lunch_type 4 388.3 84379 3014.1
## + gender:parent_marital_status 3 70.7 84697 3014.4
## + parent_educ:wkly_study_hours 10 2035.7 82732 3014.5
## + parent_educ:transport_means 5 615.3 84152 3014.6
## + parent_marital_status:practice_sport 6 773.3 83994 3015.4
## + parent_educ:lunch_type 5 477.7 84290 3015.5
## + ethnic_group:is_first_child 4 188.4 84579 3015.5
## + parent_educ:test_prep 5 338.3 84429 3016.5
## + ethnic_group:practice_sport 8 1107.8 83660 3017.1
## + ethnic_group:parent_marital_status 11 1856.5 82911 3017.8
## + ethnic_group:wkly_study_hours 8 765.8 84002 3019.5
## + ethnic_group:parent_educ 20 2002.1 82765 3034.8
## - parent_educ 5 9294.5 94062 3060.2
## - test_prep 1 9780.6 94548 3071.3
## - gender 1 12516.7 97284 3088.1
summary(stepwise_model_write)
##
## Call:
## lm(formula = writing_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours,
## data = df_4_mdl_write)
##
## Residuals:
## Min 1Q Median 3Q Max
## -48.763 -7.903 0.888 8.581 28.915
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 67.70191 5.43878
## gendermale -9.60342 1.06468
## ethnic_groupgroup B 2.66505 3.60266
## ethnic_groupgroup C 4.66371 3.29737
## ethnic_groupgroup D 6.89890 3.37504
## ethnic_groupgroup E 12.97757 3.72825
## parent_educbachelor's degree 3.78448 1.87145
## parent_educhigh school -6.78406 1.62165
## parent_educmaster's degree 5.13686 2.33681
## parent_educsome college -1.61594 1.62678
## parent_educsome high school -6.56468 1.63632
## lunch_typestandard 1.01145 3.66619
## test_prepnone -8.81344 1.10535
## parent_marital_statusmarried 7.41012 3.91977
## parent_marital_statussingle -3.99879 4.28335
## parent_marital_statuswidowed 12.38775 10.44238
## practice_sportregularly -3.44862 3.11402
## practice_sportsometimes -5.25858 3.01623
## is_first_childyes 6.17523 3.24819
## transport_meansschool_bus 5.99682 3.71242
## wkly_study_hours> 10 -13.41677 4.87463
## wkly_study_hours10-May -1.32300 3.52689
## ethnic_groupgroup B:transport_meansschool_bus -6.38307 4.47966
## ethnic_groupgroup C:transport_meansschool_bus -7.47646 4.19267
## ethnic_groupgroup D:transport_meansschool_bus -2.44868 4.26882
## ethnic_groupgroup E:transport_meansschool_bus -10.30293 4.71351
## lunch_typestandard:practice_sportregularly 6.16137 3.77036
## lunch_typestandard:practice_sportsometimes 10.02195 3.67485
## lunch_typestandard:wkly_study_hours> 10 5.91877 3.33331
## lunch_typestandard:wkly_study_hours10-May -0.07475 2.59512
## parent_marital_statusmarried:is_first_childyes -7.62546 3.55928
## parent_marital_statussingle:is_first_childyes -0.73567 3.95710
## parent_marital_statuswidowed:is_first_childyes -5.74724 8.37846
## parent_marital_statusmarried:wkly_study_hours> 10 10.26572 4.74053
## parent_marital_statussingle:wkly_study_hours> 10 18.67985 5.30411
## parent_marital_statuswidowed:wkly_study_hours> 10 5.92668 13.84492
## parent_marital_statusmarried:wkly_study_hours10-May 3.32999 3.53309
## parent_marital_statussingle:wkly_study_hours10-May 8.29920 3.98905
## parent_marital_statuswidowed:wkly_study_hours10-May -0.28438 10.39843
## t value Pr(>|t|)
## (Intercept) 12.448 < 2e-16 ***
## gendermale -9.020 < 2e-16 ***
## ethnic_groupgroup B 0.740 0.459770
## ethnic_groupgroup C 1.414 0.157818
## ethnic_groupgroup D 2.044 0.041419 *
## ethnic_groupgroup E 3.481 0.000539 ***
## parent_educbachelor's degree 2.022 0.043636 *
## parent_educhigh school -4.183 3.34e-05 ***
## parent_educmaster's degree 2.198 0.028347 *
## parent_educsome college -0.993 0.320980
## parent_educsome high school -4.012 6.86e-05 ***
## lunch_typestandard 0.276 0.782738
## test_prepnone -7.973 8.95e-15 ***
## parent_marital_statusmarried 1.890 0.059222 .
## parent_marital_statussingle -0.934 0.350937
## parent_marital_statuswidowed 1.186 0.236016
## practice_sportregularly -1.107 0.268583
## practice_sportsometimes -1.743 0.081816 .
## is_first_childyes 1.901 0.057806 .
## transport_meansschool_bus 1.615 0.106809
## wkly_study_hours> 10 -2.752 0.006112 **
## wkly_study_hours10-May -0.375 0.707718
## ethnic_groupgroup B:transport_meansschool_bus -1.425 0.154752
## ethnic_groupgroup C:transport_meansschool_bus -1.783 0.075100 .
## ethnic_groupgroup D:transport_meansschool_bus -0.574 0.566459
## ethnic_groupgroup E:transport_meansschool_bus -2.186 0.029248 *
## lunch_typestandard:practice_sportregularly 1.634 0.102796
## lunch_typestandard:practice_sportsometimes 2.727 0.006592 **
## lunch_typestandard:wkly_study_hours> 10 1.776 0.076344 .
## lunch_typestandard:wkly_study_hours10-May -0.029 0.977030
## parent_marital_statusmarried:is_first_childyes -2.142 0.032597 *
## parent_marital_statussingle:is_first_childyes -0.186 0.852583
## parent_marital_statuswidowed:is_first_childyes -0.686 0.493030
## parent_marital_statusmarried:wkly_study_hours> 10 2.166 0.030776 *
## parent_marital_statussingle:wkly_study_hours> 10 3.522 0.000464 ***
## parent_marital_statuswidowed:wkly_study_hours> 10 0.428 0.668763
## parent_marital_statusmarried:wkly_study_hours10-May 0.943 0.346342
## parent_marital_statussingle:wkly_study_hours10-May 2.080 0.037941 *
## parent_marital_statuswidowed:wkly_study_hours10-May -0.027 0.978192
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.4 on 551 degrees of freedom
## Multiple R-squared: 0.4032, Adjusted R-squared: 0.362
## F-statistic: 9.796 on 38 and 551 DF, p-value: < 2.2e-16
MAth Score
df_4_mdl_math=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,math_score)
full_fit_math=lm(math_score ~ .^2,data=df_4_mdl_math)
summary(full_fit_math)
##
## Call:
## lm(formula = math_score ~ .^2, data = df_4_mdl_math)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.489 -7.390 0.168 7.221 24.154
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 68.0411 17.6110
## gendermale 4.9827 8.9723
## ethnic_groupgroup B -20.0944 15.1422
## ethnic_groupgroup C -26.3767 14.2851
## ethnic_groupgroup D -16.7609 15.5502
## ethnic_groupgroup E -2.1592 14.5735
## parent_educbachelor's degree 33.6079 15.9209
## parent_educhigh school 12.3061 13.1796
## parent_educmaster's degree -25.1426 21.7572
## parent_educsome college -3.3640 12.9319
## parent_educsome high school 1.5736 12.5441
## lunch_typestandard 2.2940 8.9077
## test_prepnone -16.5825 9.2941
## parent_marital_statusmarried 11.4586 11.8338
## parent_marital_statussingle 7.8399 14.2425
## parent_marital_statuswidowed 56.5536 42.0759
## practice_sportregularly -29.8202 14.1677
## practice_sportsometimes -20.2458 14.0961
## is_first_childyes 13.1687 10.2054
## transport_meansschool_bus -3.8403 9.0340
## wkly_study_hours> 10 -10.7976 13.9166
## wkly_study_hours10-May 4.6821 11.1838
## gendermale:ethnic_groupgroup B 5.2886 5.6833
## gendermale:ethnic_groupgroup C 10.1735 5.4655
## gendermale:ethnic_groupgroup D 4.3097 5.4293
## gendermale:ethnic_groupgroup E 6.3964 6.0199
## gendermale:parent_educbachelor's degree -4.5741 4.7806
## gendermale:parent_educhigh school 1.1545 3.8987
## gendermale:parent_educmaster's degree 11.0840 6.6935
## gendermale:parent_educsome college -4.4251 4.0942
## gendermale:parent_educsome high school 1.5882 4.0216
## gendermale:lunch_typestandard -2.4581 2.7927
## gendermale:test_prepnone 0.3238 2.7833
## gendermale:parent_marital_statusmarried -2.2028 3.9676
## gendermale:parent_marital_statussingle -1.7229 4.4981
## gendermale:parent_marital_statuswidowed -1.1049 19.4773
## gendermale:practice_sportregularly -3.5415 4.7295
## gendermale:practice_sportsometimes -3.5726 4.7543
## gendermale:is_first_childyes 2.6976 2.9215
## gendermale:transport_meansschool_bus -0.3742 2.7006
## gendermale:wkly_study_hours> 10 -3.4820 4.2367
## gendermale:wkly_study_hours10-May -1.9685 3.2131
## ethnic_groupgroup B:parent_educbachelor's degree -4.2231 13.2581
## ethnic_groupgroup C:parent_educbachelor's degree -3.7714 13.2368
## ethnic_groupgroup D:parent_educbachelor's degree -1.2605 13.1369
## ethnic_groupgroup E:parent_educbachelor's degree -9.8679 14.9506
## ethnic_groupgroup B:parent_educhigh school -12.1115 8.3005
## ethnic_groupgroup C:parent_educhigh school -7.8179 7.9780
## ethnic_groupgroup D:parent_educhigh school -4.1223 8.1111
## ethnic_groupgroup E:parent_educhigh school -7.1674 9.0331
## ethnic_groupgroup B:parent_educmaster's degree 6.1658 15.9289
## ethnic_groupgroup C:parent_educmaster's degree -5.7091 14.7953
## ethnic_groupgroup D:parent_educmaster's degree 2.3388 15.0307
## ethnic_groupgroup E:parent_educmaster's degree -0.8632 15.8151
## ethnic_groupgroup B:parent_educsome college 2.3899 9.1796
## ethnic_groupgroup C:parent_educsome college 3.2541 8.6646
## ethnic_groupgroup D:parent_educsome college 12.0158 9.0246
## ethnic_groupgroup E:parent_educsome college 1.8215 9.1236
## ethnic_groupgroup B:parent_educsome high school -15.0749 8.7983
## ethnic_groupgroup C:parent_educsome high school -4.9385 8.2551
## ethnic_groupgroup D:parent_educsome high school -1.1085 8.3094
## ethnic_groupgroup E:parent_educsome high school 2.2394 8.9218
## ethnic_groupgroup B:lunch_typestandard 3.7732 5.9098
## ethnic_groupgroup C:lunch_typestandard 7.9926 5.7317
## ethnic_groupgroup D:lunch_typestandard 4.4950 5.6419
## ethnic_groupgroup E:lunch_typestandard 0.8425 6.5383
## ethnic_groupgroup B:test_prepnone 2.4360 6.0294
## ethnic_groupgroup C:test_prepnone 7.7889 5.6560
## ethnic_groupgroup D:test_prepnone 7.7952 5.6674
## ethnic_groupgroup E:test_prepnone 11.4896 6.1691
## ethnic_groupgroup B:parent_marital_statusmarried 4.5004 8.1401
## ethnic_groupgroup C:parent_marital_statusmarried 2.5638 7.4956
## ethnic_groupgroup D:parent_marital_statusmarried -8.5771 7.3930
## ethnic_groupgroup E:parent_marital_statusmarried -2.5010 8.1793
## ethnic_groupgroup B:parent_marital_statussingle 11.3279 9.6376
## ethnic_groupgroup C:parent_marital_statussingle 3.2686 9.1120
## ethnic_groupgroup D:parent_marital_statussingle -2.3267 8.8048
## ethnic_groupgroup E:parent_marital_statussingle 6.0944 10.1485
## ethnic_groupgroup B:parent_marital_statuswidowed 112.2530 107.8327
## ethnic_groupgroup C:parent_marital_statuswidowed 143.7513 87.6384
## ethnic_groupgroup D:parent_marital_statuswidowed 31.6392 88.3465
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 18.1643 10.7978
## ethnic_groupgroup C:practice_sportregularly 15.6305 10.7005
## ethnic_groupgroup D:practice_sportregularly 15.7111 11.9445
## ethnic_groupgroup E:practice_sportregularly 16.2136 10.9347
## ethnic_groupgroup B:practice_sportsometimes 12.2733 11.5184
## ethnic_groupgroup C:practice_sportsometimes 18.8952 11.2034
## ethnic_groupgroup D:practice_sportsometimes 12.8401 12.3508
## ethnic_groupgroup E:practice_sportsometimes 11.3892 11.2604
## ethnic_groupgroup B:is_first_childyes 10.2091 5.9835
## ethnic_groupgroup C:is_first_childyes -0.1812 5.6444
## ethnic_groupgroup D:is_first_childyes 1.1359 5.7099
## ethnic_groupgroup E:is_first_childyes 3.4944 6.4312
## ethnic_groupgroup B:transport_meansschool_bus -4.0964 5.9868
## ethnic_groupgroup C:transport_meansschool_bus -10.1575 5.5281
## ethnic_groupgroup D:transport_meansschool_bus -2.9759 5.5226
## ethnic_groupgroup E:transport_meansschool_bus -11.7574 6.5192
## ethnic_groupgroup B:wkly_study_hours> 10 -10.0294 10.1919
## ethnic_groupgroup C:wkly_study_hours> 10 1.4113 10.0649
## ethnic_groupgroup D:wkly_study_hours> 10 4.1762 10.0509
## ethnic_groupgroup E:wkly_study_hours> 10 -3.4964 10.9491
## ethnic_groupgroup B:wkly_study_hours10-May -5.9718 8.5598
## ethnic_groupgroup C:wkly_study_hours10-May 2.3955 8.3758
## ethnic_groupgroup D:wkly_study_hours10-May 2.5625 8.5173
## ethnic_groupgroup E:wkly_study_hours10-May -2.6577 9.1705
## parent_educbachelor's degree:lunch_typestandard 2.1141 5.1441
## parent_educhigh school:lunch_typestandard 0.3684 4.1512
## parent_educmaster's degree:lunch_typestandard 9.9274 7.6084
## parent_educsome college:lunch_typestandard 3.3042 4.1848
## parent_educsome high school:lunch_typestandard 5.5345 4.3349
## parent_educbachelor's degree:test_prepnone -3.9833 4.7464
## parent_educhigh school:test_prepnone -1.1824 4.5458
## parent_educmaster's degree:test_prepnone -1.8200 8.0921
## parent_educsome college:test_prepnone -2.3529 4.2606
## parent_educsome high school:test_prepnone 3.0111 4.1206
## parent_educbachelor's degree:parent_marital_statusmarried -17.7590 8.4713
## parent_educhigh school:parent_marital_statusmarried 1.5718 5.9578
## parent_educmaster's degree:parent_marital_statusmarried 2.1560 8.6196
## parent_educsome college:parent_marital_statusmarried -8.3928 5.8669
## parent_educsome high school:parent_marital_statusmarried -7.8355 5.7817
## parent_educbachelor's degree:parent_marital_statussingle -19.7203 9.1319
## parent_educhigh school:parent_marital_statussingle 3.9993 6.5081
## parent_educmaster's degree:parent_marital_statussingle -1.7191 9.2012
## parent_educsome college:parent_marital_statussingle -9.4469 6.5341
## parent_educsome high school:parent_marital_statussingle -9.7176 6.4548
## parent_educbachelor's degree:parent_marital_statuswidowed -38.7612 89.7785
## parent_educhigh school:parent_marital_statuswidowed -117.8054 98.7809
## parent_educmaster's degree:parent_marital_statuswidowed -110.3756 51.7457
## parent_educsome college:parent_marital_statuswidowed -114.0106 64.8797
## parent_educsome high school:parent_marital_statuswidowed -92.5395 77.7614
## parent_educbachelor's degree:practice_sportregularly -3.7294 8.7461
## parent_educhigh school:practice_sportregularly -13.6445 7.5268
## parent_educmaster's degree:practice_sportregularly 0.7016 10.6360
## parent_educsome college:practice_sportregularly -0.2142 7.6542
## parent_educsome high school:practice_sportregularly -2.7852 7.3917
## parent_educbachelor's degree:practice_sportsometimes -12.4201 8.3926
## parent_educhigh school:practice_sportsometimes -13.5033 7.1288
## parent_educmaster's degree:practice_sportsometimes 9.0615 8.8601
## parent_educsome college:practice_sportsometimes 1.2774 7.3663
## parent_educsome high school:practice_sportsometimes 0.4391 6.9262
## parent_educbachelor's degree:is_first_childyes 2.0649 5.1938
## parent_educhigh school:is_first_childyes 8.6134 4.4335
## parent_educmaster's degree:is_first_childyes 6.7664 7.7546
## parent_educsome college:is_first_childyes 9.2132 4.3295
## parent_educsome high school:is_first_childyes 4.6542 4.3602
## parent_educbachelor's degree:transport_meansschool_bus 5.4304 5.1849
## parent_educhigh school:transport_meansschool_bus 4.0937 4.1394
## parent_educmaster's degree:transport_meansschool_bus 11.6831 6.3824
## parent_educsome college:transport_meansschool_bus 4.9041 4.2151
## parent_educsome high school:transport_meansschool_bus 6.9767 4.2890
## parent_educbachelor's degree:wkly_study_hours> 10 -14.7410 7.6498
## parent_educhigh school:wkly_study_hours> 10 -10.1303 6.3679
## parent_educmaster's degree:wkly_study_hours> 10 6.3671 13.7791
## parent_educsome college:wkly_study_hours> 10 -7.2539 6.4097
## parent_educsome high school:wkly_study_hours> 10 -11.3467 6.5283
## parent_educbachelor's degree:wkly_study_hours10-May -3.4329 5.3169
## parent_educhigh school:wkly_study_hours10-May -9.6586 4.9571
## parent_educmaster's degree:wkly_study_hours10-May 0.9849 7.0888
## parent_educsome college:wkly_study_hours10-May -3.5554 5.0476
## parent_educsome high school:wkly_study_hours10-May -10.4143 5.3257
## lunch_typestandard:test_prepnone -1.9452 3.1136
## lunch_typestandard:parent_marital_statusmarried -6.2756 4.0742
## lunch_typestandard:parent_marital_statussingle -2.2019 4.7175
## lunch_typestandard:parent_marital_statuswidowed -21.8879 80.6364
## lunch_typestandard:practice_sportregularly 10.3501 5.3704
## lunch_typestandard:practice_sportsometimes 11.0341 5.1768
## lunch_typestandard:is_first_childyes 0.1283 3.1548
## lunch_typestandard:transport_meansschool_bus -2.5076 2.8951
## lunch_typestandard:wkly_study_hours> 10 5.7376 4.4178
## lunch_typestandard:wkly_study_hours10-May 0.5929 3.3046
## test_prepnone:parent_marital_statusmarried 5.6467 4.1442
## test_prepnone:parent_marital_statussingle 2.5438 4.7712
## test_prepnone:parent_marital_statuswidowed -70.1691 42.1289
## test_prepnone:practice_sportregularly 1.5825 5.1802
## test_prepnone:practice_sportsometimes 3.1630 5.0767
## test_prepnone:is_first_childyes -0.6723 3.1267
## test_prepnone:transport_meansschool_bus 0.4150 2.8429
## test_prepnone:wkly_study_hours> 10 -4.6995 4.4626
## test_prepnone:wkly_study_hours10-May 1.6772 3.5219
## parent_marital_statusmarried:practice_sportregularly 9.1006 6.6592
## parent_marital_statussingle:practice_sportregularly 2.6152 8.7085
## parent_marital_statuswidowed:practice_sportregularly 22.5587 85.2725
## parent_marital_statusmarried:practice_sportsometimes 5.1124 6.5673
## parent_marital_statussingle:practice_sportsometimes -1.6116 8.5136
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -12.7542 4.8986
## parent_marital_statussingle:is_first_childyes -4.9445 5.4292
## parent_marital_statuswidowed:is_first_childyes 47.8196 30.2193
## parent_marital_statusmarried:transport_meansschool_bus 4.6203 4.0454
## parent_marital_statussingle:transport_meansschool_bus -2.0235 4.6103
## parent_marital_statuswidowed:transport_meansschool_bus -34.0699 19.6388
## parent_marital_statusmarried:wkly_study_hours> 10 18.1048 6.3197
## parent_marital_statussingle:wkly_study_hours> 10 21.8022 7.0282
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 1.2179 4.6394
## parent_marital_statussingle:wkly_study_hours10-May 3.3543 5.1241
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -3.3085 6.0157
## practice_sportsometimes:is_first_childyes -5.4272 5.8699
## practice_sportregularly:transport_meansschool_bus 9.9774 5.0267
## practice_sportsometimes:transport_meansschool_bus 5.9885 4.8789
## practice_sportregularly:wkly_study_hours> 10 2.6252 7.1266
## practice_sportsometimes:wkly_study_hours> 10 2.0680 6.9901
## practice_sportregularly:wkly_study_hours10-May 7.8713 5.4844
## practice_sportsometimes:wkly_study_hours10-May 2.5781 5.4074
## is_first_childyes:transport_meansschool_bus -5.3887 3.0599
## is_first_childyes:wkly_study_hours> 10 2.8322 4.6001
## is_first_childyes:wkly_study_hours10-May -4.9634 3.4724
## transport_meansschool_bus:wkly_study_hours> 10 4.0303 4.4205
## transport_meansschool_bus:wkly_study_hours10-May 2.7910 3.1920
## t value Pr(>|t|)
## (Intercept) 3.864 0.000131 ***
## gendermale 0.555 0.578989
## ethnic_groupgroup B -1.327 0.185283
## ethnic_groupgroup C -1.846 0.065599 .
## ethnic_groupgroup D -1.078 0.281775
## ethnic_groupgroup E -0.148 0.882295
## parent_educbachelor's degree 2.111 0.035426 *
## parent_educhigh school 0.934 0.351036
## parent_educmaster's degree -1.156 0.248565
## parent_educsome college -0.260 0.794902
## parent_educsome high school 0.125 0.900238
## lunch_typestandard 0.258 0.796904
## test_prepnone -1.784 0.075183 .
## parent_marital_statusmarried 0.968 0.333510
## parent_marital_statussingle 0.550 0.582326
## parent_marital_statuswidowed 1.344 0.179717
## practice_sportregularly -2.105 0.035959 *
## practice_sportsometimes -1.436 0.151741
## is_first_childyes 1.290 0.197701
## transport_meansschool_bus -0.425 0.671008
## wkly_study_hours> 10 -0.776 0.438299
## wkly_study_hours10-May 0.419 0.675703
## gendermale:ethnic_groupgroup B 0.931 0.352678
## gendermale:ethnic_groupgroup C 1.861 0.063454 .
## gendermale:ethnic_groupgroup D 0.794 0.427811
## gendermale:ethnic_groupgroup E 1.063 0.288659
## gendermale:parent_educbachelor's degree -0.957 0.339269
## gendermale:parent_educhigh school 0.296 0.767289
## gendermale:parent_educmaster's degree 1.656 0.098552 .
## gendermale:parent_educsome college -1.081 0.280453
## gendermale:parent_educsome high school 0.395 0.693115
## gendermale:lunch_typestandard -0.880 0.379317
## gendermale:test_prepnone 0.116 0.907448
## gendermale:parent_marital_statusmarried -0.555 0.579095
## gendermale:parent_marital_statussingle -0.383 0.701904
## gendermale:parent_marital_statuswidowed -0.057 0.954790
## gendermale:practice_sportregularly -0.749 0.454437
## gendermale:practice_sportsometimes -0.751 0.452841
## gendermale:is_first_childyes 0.923 0.356397
## gendermale:transport_meansschool_bus -0.139 0.889859
## gendermale:wkly_study_hours> 10 -0.822 0.411658
## gendermale:wkly_study_hours10-May -0.613 0.540476
## ethnic_groupgroup B:parent_educbachelor's degree -0.319 0.750255
## ethnic_groupgroup C:parent_educbachelor's degree -0.285 0.775863
## ethnic_groupgroup D:parent_educbachelor's degree -0.096 0.923607
## ethnic_groupgroup E:parent_educbachelor's degree -0.660 0.509629
## ethnic_groupgroup B:parent_educhigh school -1.459 0.145350
## ethnic_groupgroup C:parent_educhigh school -0.980 0.327741
## ethnic_groupgroup D:parent_educhigh school -0.508 0.611582
## ethnic_groupgroup E:parent_educhigh school -0.793 0.428002
## ethnic_groupgroup B:parent_educmaster's degree 0.387 0.698911
## ethnic_groupgroup C:parent_educmaster's degree -0.386 0.699808
## ethnic_groupgroup D:parent_educmaster's degree 0.156 0.876431
## ethnic_groupgroup E:parent_educmaster's degree -0.055 0.956503
## ethnic_groupgroup B:parent_educsome college 0.260 0.794732
## ethnic_groupgroup C:parent_educsome college 0.376 0.707455
## ethnic_groupgroup D:parent_educsome college 1.331 0.183836
## ethnic_groupgroup E:parent_educsome college 0.200 0.841866
## ethnic_groupgroup B:parent_educsome high school -1.713 0.087450 .
## ethnic_groupgroup C:parent_educsome high school -0.598 0.550037
## ethnic_groupgroup D:parent_educsome high school -0.133 0.893944
## ethnic_groupgroup E:parent_educsome high school 0.251 0.801944
## ethnic_groupgroup B:lunch_typestandard 0.638 0.523555
## ethnic_groupgroup C:lunch_typestandard 1.394 0.163987
## ethnic_groupgroup D:lunch_typestandard 0.797 0.426112
## ethnic_groupgroup E:lunch_typestandard 0.129 0.897536
## ethnic_groupgroup B:test_prepnone 0.404 0.686423
## ethnic_groupgroup C:test_prepnone 1.377 0.169289
## ethnic_groupgroup D:test_prepnone 1.375 0.169796
## ethnic_groupgroup E:test_prepnone 1.862 0.063307 .
## ethnic_groupgroup B:parent_marital_statusmarried 0.553 0.580679
## ethnic_groupgroup C:parent_marital_statusmarried 0.342 0.732511
## ethnic_groupgroup D:parent_marital_statusmarried -1.160 0.246704
## ethnic_groupgroup E:parent_marital_statusmarried -0.306 0.759941
## ethnic_groupgroup B:parent_marital_statussingle 1.175 0.240572
## ethnic_groupgroup C:parent_marital_statussingle 0.359 0.720004
## ethnic_groupgroup D:parent_marital_statussingle -0.264 0.791728
## ethnic_groupgroup E:parent_marital_statussingle 0.601 0.548513
## ethnic_groupgroup B:parent_marital_statuswidowed 1.041 0.298536
## ethnic_groupgroup C:parent_marital_statuswidowed 1.640 0.101768
## ethnic_groupgroup D:parent_marital_statuswidowed 0.358 0.720446
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 1.682 0.093341 .
## ethnic_groupgroup C:practice_sportregularly 1.461 0.144908
## ethnic_groupgroup D:practice_sportregularly 1.315 0.189183
## ethnic_groupgroup E:practice_sportregularly 1.483 0.138959
## ethnic_groupgroup B:practice_sportsometimes 1.066 0.287304
## ethnic_groupgroup C:practice_sportsometimes 1.687 0.092504 .
## ethnic_groupgroup D:practice_sportsometimes 1.040 0.299174
## ethnic_groupgroup E:practice_sportsometimes 1.011 0.312443
## ethnic_groupgroup B:is_first_childyes 1.706 0.088779 .
## ethnic_groupgroup C:is_first_childyes -0.032 0.974411
## ethnic_groupgroup D:is_first_childyes 0.199 0.842418
## ethnic_groupgroup E:is_first_childyes 0.543 0.587200
## ethnic_groupgroup B:transport_meansschool_bus -0.684 0.494241
## ethnic_groupgroup C:transport_meansschool_bus -1.837 0.066921 .
## ethnic_groupgroup D:transport_meansschool_bus -0.539 0.590297
## ethnic_groupgroup E:transport_meansschool_bus -1.804 0.072093 .
## ethnic_groupgroup B:wkly_study_hours> 10 -0.984 0.325710
## ethnic_groupgroup C:wkly_study_hours> 10 0.140 0.888562
## ethnic_groupgroup D:wkly_study_hours> 10 0.416 0.678007
## ethnic_groupgroup E:wkly_study_hours> 10 -0.319 0.749646
## ethnic_groupgroup B:wkly_study_hours10-May -0.698 0.485813
## ethnic_groupgroup C:wkly_study_hours10-May 0.286 0.775035
## ethnic_groupgroup D:wkly_study_hours10-May 0.301 0.763685
## ethnic_groupgroup E:wkly_study_hours10-May -0.290 0.772121
## parent_educbachelor's degree:lunch_typestandard 0.411 0.681330
## parent_educhigh school:lunch_typestandard 0.089 0.929339
## parent_educmaster's degree:lunch_typestandard 1.305 0.192749
## parent_educsome college:lunch_typestandard 0.790 0.430256
## parent_educsome high school:lunch_typestandard 1.277 0.202472
## parent_educbachelor's degree:test_prepnone -0.839 0.401869
## parent_educhigh school:test_prepnone -0.260 0.794920
## parent_educmaster's degree:test_prepnone -0.225 0.822173
## parent_educsome college:test_prepnone -0.552 0.581102
## parent_educsome high school:test_prepnone 0.731 0.465380
## parent_educbachelor's degree:parent_marital_statusmarried -2.096 0.036705 *
## parent_educhigh school:parent_marital_statusmarried 0.264 0.792052
## parent_educmaster's degree:parent_marital_statusmarried 0.250 0.802627
## parent_educsome college:parent_marital_statusmarried -1.431 0.153379
## parent_educsome high school:parent_marital_statusmarried -1.355 0.176143
## parent_educbachelor's degree:parent_marital_statussingle -2.160 0.031431 *
## parent_educhigh school:parent_marital_statussingle 0.615 0.539246
## parent_educmaster's degree:parent_marital_statussingle -0.187 0.851886
## parent_educsome college:parent_marital_statussingle -1.446 0.149058
## parent_educsome high school:parent_marital_statussingle -1.505 0.133023
## parent_educbachelor's degree:parent_marital_statuswidowed -0.432 0.666171
## parent_educhigh school:parent_marital_statuswidowed -1.193 0.233767
## parent_educmaster's degree:parent_marital_statuswidowed -2.133 0.033557 *
## parent_educsome college:parent_marital_statuswidowed -1.757 0.079672 .
## parent_educsome high school:parent_marital_statuswidowed -1.190 0.234766
## parent_educbachelor's degree:practice_sportregularly -0.426 0.670053
## parent_educhigh school:practice_sportregularly -1.813 0.070647 .
## parent_educmaster's degree:practice_sportregularly 0.066 0.947437
## parent_educsome college:practice_sportregularly -0.028 0.977692
## parent_educsome high school:practice_sportregularly -0.377 0.706532
## parent_educbachelor's degree:practice_sportsometimes -1.480 0.139724
## parent_educhigh school:practice_sportsometimes -1.894 0.058951 .
## parent_educmaster's degree:practice_sportsometimes 1.023 0.307081
## parent_educsome college:practice_sportsometimes 0.173 0.862420
## parent_educsome high school:practice_sportsometimes 0.063 0.949489
## parent_educbachelor's degree:is_first_childyes 0.398 0.691162
## parent_educhigh school:is_first_childyes 1.943 0.052773 .
## parent_educmaster's degree:is_first_childyes 0.873 0.383445
## parent_educsome college:is_first_childyes 2.128 0.033972 *
## parent_educsome high school:is_first_childyes 1.067 0.286450
## parent_educbachelor's degree:transport_meansschool_bus 1.047 0.295600
## parent_educhigh school:transport_meansschool_bus 0.989 0.323307
## parent_educmaster's degree:transport_meansschool_bus 1.831 0.067950 .
## parent_educsome college:transport_meansschool_bus 1.163 0.245371
## parent_educsome high school:transport_meansschool_bus 1.627 0.104635
## parent_educbachelor's degree:wkly_study_hours> 10 -1.927 0.054721 .
## parent_educhigh school:wkly_study_hours> 10 -1.591 0.112471
## parent_educmaster's degree:wkly_study_hours> 10 0.462 0.644281
## parent_educsome college:wkly_study_hours> 10 -1.132 0.258463
## parent_educsome high school:wkly_study_hours> 10 -1.738 0.083002 .
## parent_educbachelor's degree:wkly_study_hours10-May -0.646 0.518891
## parent_educhigh school:wkly_study_hours10-May -1.948 0.052093 .
## parent_educmaster's degree:wkly_study_hours10-May 0.139 0.889578
## parent_educsome college:wkly_study_hours10-May -0.704 0.481637
## parent_educsome high school:wkly_study_hours10-May -1.955 0.051251 .
## lunch_typestandard:test_prepnone -0.625 0.532521
## lunch_typestandard:parent_marital_statusmarried -1.540 0.124305
## lunch_typestandard:parent_marital_statussingle -0.467 0.640946
## lunch_typestandard:parent_marital_statuswidowed -0.271 0.786200
## lunch_typestandard:practice_sportregularly 1.927 0.054686 .
## lunch_typestandard:practice_sportsometimes 2.131 0.033689 *
## lunch_typestandard:is_first_childyes 0.041 0.967588
## lunch_typestandard:transport_meansschool_bus -0.866 0.386933
## lunch_typestandard:wkly_study_hours> 10 1.299 0.194815
## lunch_typestandard:wkly_study_hours10-May 0.179 0.857717
## test_prepnone:parent_marital_statusmarried 1.363 0.173819
## test_prepnone:parent_marital_statussingle 0.533 0.594231
## test_prepnone:parent_marital_statuswidowed -1.666 0.096615 .
## test_prepnone:practice_sportregularly 0.305 0.760155
## test_prepnone:practice_sportsometimes 0.623 0.533633
## test_prepnone:is_first_childyes -0.215 0.829855
## test_prepnone:transport_meansschool_bus 0.146 0.884028
## test_prepnone:wkly_study_hours> 10 -1.053 0.292966
## test_prepnone:wkly_study_hours10-May 0.476 0.634185
## parent_marital_statusmarried:practice_sportregularly 1.367 0.172546
## parent_marital_statussingle:practice_sportregularly 0.300 0.764107
## parent_marital_statuswidowed:practice_sportregularly 0.265 0.791500
## parent_marital_statusmarried:practice_sportsometimes 0.778 0.436770
## parent_marital_statussingle:practice_sportsometimes -0.189 0.849955
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -2.604 0.009583 **
## parent_marital_statussingle:is_first_childyes -0.911 0.363014
## parent_marital_statuswidowed:is_first_childyes 1.582 0.114379
## parent_marital_statusmarried:transport_meansschool_bus 1.142 0.254126
## parent_marital_statussingle:transport_meansschool_bus -0.439 0.660982
## parent_marital_statuswidowed:transport_meansschool_bus -1.735 0.083576 .
## parent_marital_statusmarried:wkly_study_hours> 10 2.865 0.004403 **
## parent_marital_statussingle:wkly_study_hours> 10 3.102 0.002064 **
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 0.263 0.793062
## parent_marital_statussingle:wkly_study_hours10-May 0.655 0.513103
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -0.550 0.582650
## practice_sportsometimes:is_first_childyes -0.925 0.355759
## practice_sportregularly:transport_meansschool_bus 1.985 0.047872 *
## practice_sportsometimes:transport_meansschool_bus 1.227 0.220411
## practice_sportregularly:wkly_study_hours> 10 0.368 0.712800
## practice_sportsometimes:wkly_study_hours> 10 0.296 0.767511
## practice_sportregularly:wkly_study_hours10-May 1.435 0.152043
## practice_sportsometimes:wkly_study_hours10-May 0.477 0.633796
## is_first_childyes:transport_meansschool_bus -1.761 0.079028 .
## is_first_childyes:wkly_study_hours> 10 0.616 0.538468
## is_first_childyes:wkly_study_hours10-May -1.429 0.153714
## transport_meansschool_bus:wkly_study_hours> 10 0.912 0.362481
## transport_meansschool_bus:wkly_study_hours10-May 0.874 0.382459
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.21 on 383 degrees of freedom
## Multiple R-squared: 0.5635, Adjusted R-squared: 0.3287
## F-statistic: 2.4 on 206 and 383 DF, p-value: 7.833e-14
stepwise_model_math <- step(full_fit_math, direction = "both", trace = 1)
## Start: AIC=3204.25
## math_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours)^2
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_educ 20 3316.3 70110 3192.8
## - parent_educ:test_prep 5 440.1 67234 3198.1
## - gender:parent_marital_status 3 54.0 66847 3198.7
## - parent_educ:lunch_type 5 591.2 67385 3199.4
## - ethnic_group:wkly_study_hours 8 1323.8 68117 3199.8
## - parent_educ:wkly_study_hours 10 1801.1 68595 3199.9
## - test_prep:practice_sport 2 93.5 66887 3201.1
## - parent_marital_status:practice_sport 4 550.9 67344 3201.1
## - gender:practice_sport 2 107.4 66901 3201.2
## - gender:wkly_study_hours 2 123.6 66917 3201.3
## - parent_educ:transport_means 5 809.3 67603 3201.4
## - ethnic_group:lunch_type 4 591.0 67384 3201.4
## - transport_means:wkly_study_hours 2 187.6 66981 3201.9
## - practice_sport:is_first_child 2 198.4 66992 3202.0
## - lunch_type:is_first_child 1 0.3 66794 3202.3
## - gender:test_prep 1 2.4 66796 3202.3
## - gender:transport_means 1 3.3 66797 3202.3
## - test_prep:transport_means 1 3.7 66797 3202.3
## - test_prep:is_first_child 1 8.1 66802 3202.3
## - practice_sport:wkly_study_hours 4 718.0 67511 3202.6
## - lunch_type:test_prep 1 68.1 66862 3202.9
## - ethnic_group:practice_sport 8 1701.9 68495 3203.1
## - lunch_type:wkly_study_hours 2 352.3 67146 3203.4
## - lunch_type:transport_means 1 130.8 66924 3203.4
## - gender:lunch_type 1 135.1 66929 3203.4
## - gender:is_first_child 1 148.7 66942 3203.6
## - test_prep:parent_marital_status 2 403.4 67197 3203.8
## - gender:ethnic_group 4 869.6 67663 3203.9
## - parent_educ:is_first_child 5 1132.1 67926 3204.2
## <none> 66793 3204.3
## - gender:parent_educ 5 1173.5 67967 3204.5
## - test_prep:wkly_study_hours 2 516.4 67310 3204.8
## - ethnic_group:parent_marital_status 9 2150.3 68944 3204.9
## - lunch_type:parent_marital_status 2 552.7 67346 3205.1
## - ethnic_group:test_prep 4 1027.0 67820 3205.3
## - parent_educ:practice_sport 10 2545.2 69339 3206.3
## - ethnic_group:is_first_child 4 1194.4 67988 3206.7
## - parent_educ:parent_marital_status 13 3334.3 70128 3207.0
## - is_first_child:transport_means 1 540.9 67334 3207.0
## - practice_sport:transport_means 2 773.2 67567 3207.0
## - is_first_child:wkly_study_hours 2 781.2 67575 3207.1
## - lunch_type:practice_sport 2 806.9 67600 3207.3
## - ethnic_group:transport_means 4 1369.9 68163 3208.2
## - parent_marital_status:transport_means 3 1399.6 68193 3210.5
## - parent_marital_status:wkly_study_hours 4 2104.0 68897 3214.5
## - parent_marital_status:is_first_child 2 1736.9 68530 3215.4
##
## Step: AIC=3192.84
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 1343.3 71453 3184.0
## - ethnic_group:wkly_study_hours 8 963.6 71073 3184.9
## - parent_educ:test_prep 5 338.0 70448 3185.7
## - parent_educ:lunch_type 5 451.8 70562 3186.6
## - gender:parent_marital_status 3 77.7 70187 3187.5
## - ethnic_group:practice_sport 8 1396.5 71506 3188.5
## - parent_marital_status:practice_sport 4 526.1 70636 3189.3
## - gender:wkly_study_hours 2 84.8 70194 3189.6
## - test_prep:practice_sport 2 90.5 70200 3189.6
## - parent_educ:transport_means 5 905.7 71015 3190.4
## - practice_sport:is_first_child 2 203.1 70313 3190.5
## - ethnic_group:lunch_type 4 690.5 70800 3190.6
## - gender:practice_sport 2 238.2 70348 3190.8
## - lunch_type:is_first_child 1 0.2 70110 3190.8
## - gender:transport_means 1 0.2 70110 3190.8
## - lunch_type:test_prep 1 1.0 70111 3190.8
## - gender:test_prep 1 6.0 70116 3190.9
## - test_prep:transport_means 1 13.7 70123 3191.0
## - gender:is_first_child 1 26.2 70136 3191.1
## - test_prep:is_first_child 1 33.4 70143 3191.1
## - lunch_type:parent_marital_status 2 291.9 70402 3191.3
## - gender:lunch_type 1 114.9 70225 3191.8
## - ethnic_group:test_prep 4 836.4 70946 3191.8
## - transport_means:wkly_study_hours 2 360.6 70470 3191.9
## - practice_sport:wkly_study_hours 4 853.3 70963 3192.0
## - parent_educ:is_first_child 5 1098.4 71208 3192.0
## - gender:ethnic_group 4 860.5 70970 3192.0
## - test_prep:parent_marital_status 2 402.3 70512 3192.2
## - gender:parent_educ 5 1125.5 71235 3192.2
## - lunch_type:transport_means 1 226.0 70336 3192.7
## <none> 70110 3192.8
## - lunch_type:wkly_study_hours 2 538.0 70648 3193.3
## - is_first_child:wkly_study_hours 2 543.0 70653 3193.4
## - test_prep:wkly_study_hours 2 569.9 70680 3193.6
## - ethnic_group:parent_marital_status 9 2293.6 72403 3193.8
## - parent_educ:practice_sport 10 2568.4 72678 3194.1
## - is_first_child:transport_means 1 470.4 70580 3194.8
## - practice_sport:transport_means 2 724.0 70834 3194.9
## - lunch_type:practice_sport 2 860.0 70970 3196.0
## - ethnic_group:transport_means 4 1409.3 71519 3196.6
## - parent_marital_status:transport_means 3 1169.4 71279 3196.6
## - ethnic_group:is_first_child 4 1483.9 71594 3197.2
## - parent_marital_status:wkly_study_hours 4 1669.0 71779 3198.7
## - parent_educ:parent_marital_status 13 3948.0 74058 3199.2
## - parent_marital_status:is_first_child 2 1642.9 71753 3202.5
## + ethnic_group:parent_educ 20 3316.3 66793 3204.3
##
## Step: AIC=3184.04
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:wkly_study_hours 8 1060.7 72514 3176.7
## - parent_educ:lunch_type 5 330.0 71783 3176.8
## - parent_educ:test_prep 5 395.5 71848 3177.3
## - gender:parent_marital_status 3 71.4 71524 3178.6
## - ethnic_group:practice_sport 8 1299.7 72753 3178.7
## - ethnic_group:lunch_type 4 543.5 71997 3180.5
## - parent_marital_status:practice_sport 4 607.7 72061 3181.0
## - test_prep:practice_sport 2 164.8 71618 3181.4
## - gender:wkly_study_hours 2 178.6 71632 3181.5
## - gender:practice_sport 2 193.6 71647 3181.6
## - practice_sport:is_first_child 2 204.1 71657 3181.7
## - parent_educ:transport_means 5 939.1 72392 3181.7
## - practice_sport:wkly_study_hours 4 701.9 72155 3181.8
## - lunch_type:test_prep 1 0.1 71453 3182.0
## - gender:transport_means 1 2.0 71455 3182.1
## - lunch_type:is_first_child 1 7.3 71460 3182.1
## - gender:test_prep 1 9.7 71463 3182.1
## - ethnic_group:test_prep 4 740.2 72193 3182.1
## - test_prep:is_first_child 1 16.6 71470 3182.2
## - test_prep:transport_means 1 16.8 71470 3182.2
## - gender:is_first_child 1 23.1 71476 3182.2
## - lunch_type:parent_marital_status 2 307.7 71761 3182.6
## - lunch_type:wkly_study_hours 2 327.7 71781 3182.7
## - gender:lunch_type 1 94.3 71547 3182.8
## - gender:parent_educ 5 1100.3 72553 3183.1
## - transport_means:wkly_study_hours 2 407.0 71860 3183.4
## - parent_educ:is_first_child 5 1144.4 72597 3183.4
## - is_first_child:wkly_study_hours 2 417.3 71870 3183.5
## - gender:ethnic_group 4 920.2 72373 3183.6
## - test_prep:parent_marital_status 2 440.7 71894 3183.7
## <none> 71453 3184.0
## - lunch_type:transport_means 1 318.5 71772 3184.7
## - practice_sport:transport_means 2 638.5 72091 3185.3
## - is_first_child:transport_means 1 494.4 71947 3186.1
## - ethnic_group:parent_marital_status 9 2511.3 73964 3186.4
## - ethnic_group:transport_means 4 1268.3 72721 3186.4
## - lunch_type:practice_sport 2 795.8 72249 3186.6
## - test_prep:wkly_study_hours 2 800.9 72254 3186.6
## - parent_educ:practice_sport 10 2798.9 74252 3186.7
## - parent_marital_status:transport_means 3 1242.1 72695 3188.2
## - ethnic_group:is_first_child 4 1585.3 73038 3189.0
## - parent_marital_status:wkly_study_hours 4 1707.0 73160 3190.0
## - parent_educ:parent_marital_status 13 4246.1 75699 3192.1
## + parent_educ:wkly_study_hours 10 1343.3 70110 3192.8
## - parent_marital_status:is_first_child 2 1880.9 73334 3195.4
## + ethnic_group:parent_educ 20 2858.5 68595 3199.9
##
## Step: AIC=3176.73
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:lunch_type 5 294.6 72808 3169.1
## - parent_educ:test_prep 5 425.1 72939 3170.2
## - gender:parent_marital_status 3 77.7 72591 3171.4
## - ethnic_group:practice_sport 8 1324.8 73838 3171.4
## - parent_marital_status:practice_sport 4 477.7 72991 3172.6
## - ethnic_group:lunch_type 4 592.3 73106 3173.5
## - parent_educ:transport_means 5 852.7 73366 3173.6
## - gender:wkly_study_hours 2 138.0 72652 3173.9
## - test_prep:practice_sport 2 157.5 72671 3174.0
## - ethnic_group:test_prep 4 699.6 73213 3174.4
## - gender:practice_sport 2 212.8 72726 3174.5
## - practice_sport:wkly_study_hours 4 715.7 73229 3174.5
## - practice_sport:is_first_child 2 230.8 72744 3174.6
## - lunch_type:test_prep 1 3.8 72518 3174.8
## - gender:transport_means 1 3.8 72518 3174.8
## - transport_means:wkly_study_hours 2 251.7 72765 3174.8
## - gender:is_first_child 1 9.8 72523 3174.8
## - lunch_type:is_first_child 1 10.0 72524 3174.8
## - test_prep:transport_means 1 14.0 72528 3174.8
## - gender:test_prep 1 32.5 72546 3175.0
## - test_prep:is_first_child 1 49.0 72563 3175.1
## - gender:parent_educ 5 1062.9 73577 3175.3
## - lunch_type:parent_marital_status 2 327.1 72841 3175.4
## - gender:lunch_type 1 100.0 72614 3175.5
## - lunch_type:wkly_study_hours 2 408.7 72922 3176.0
## - gender:ethnic_group 4 915.4 73429 3176.1
## - parent_educ:is_first_child 5 1198.1 73712 3176.4
## <none> 72514 3176.7
## - test_prep:parent_marital_status 2 499.2 73013 3176.8
## - is_first_child:wkly_study_hours 2 516.9 73031 3176.9
## - lunch_type:transport_means 1 292.6 72806 3177.1
## - ethnic_group:parent_marital_status 9 2400.6 74914 3177.9
## - practice_sport:transport_means 2 658.8 73173 3178.1
## - ethnic_group:transport_means 4 1211.0 73725 3178.5
## - parent_educ:practice_sport 10 2730.9 75245 3178.5
## - is_first_child:transport_means 1 494.6 73008 3178.7
## - test_prep:wkly_study_hours 2 797.9 73312 3179.2
## - lunch_type:practice_sport 2 872.4 73386 3179.8
## - parent_marital_status:transport_means 3 1276.5 73790 3181.0
## - parent_marital_status:wkly_study_hours 4 1550.3 74064 3181.2
## - ethnic_group:is_first_child 4 1638.0 74152 3181.9
## - parent_educ:parent_marital_status 13 4105.1 76619 3183.2
## + ethnic_group:wkly_study_hours 8 1060.7 71453 3184.0
## + parent_educ:wkly_study_hours 10 1440.4 71073 3184.9
## - parent_marital_status:is_first_child 2 1784.1 74298 3187.1
## + ethnic_group:parent_educ 20 2546.0 69968 3195.6
##
## Step: AIC=3169.12
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:test_prep 5 359.4 73168 3162.0
## - ethnic_group:practice_sport 8 1287.1 74095 3163.5
## - gender:parent_marital_status 3 84.3 72893 3163.8
## - parent_marital_status:practice_sport 4 510.3 73319 3165.2
## - ethnic_group:lunch_type 4 611.1 73419 3166.1
## - gender:wkly_study_hours 2 132.3 72941 3166.2
## - test_prep:practice_sport 2 157.8 72966 3166.4
## - parent_educ:transport_means 5 914.4 73723 3166.5
## - ethnic_group:test_prep 4 686.0 73494 3166.7
## - gender:practice_sport 2 217.7 73026 3166.9
## - practice_sport:is_first_child 2 246.8 73055 3167.1
## - gender:transport_means 1 1.0 72809 3167.1
## - lunch_type:test_prep 1 1.8 72810 3167.1
## - test_prep:transport_means 1 14.7 72823 3167.2
## - lunch_type:is_first_child 1 14.9 72823 3167.2
## - practice_sport:wkly_study_hours 4 759.8 73568 3167.2
## - transport_means:wkly_study_hours 2 270.4 73079 3167.3
## - gender:is_first_child 1 30.9 72839 3167.4
## - gender:test_prep 1 38.9 72847 3167.4
## - test_prep:is_first_child 1 39.2 72847 3167.4
## - gender:parent_educ 5 1056.1 73864 3167.6
## - lunch_type:parent_marital_status 2 329.5 73138 3167.8
## - lunch_type:wkly_study_hours 2 370.3 73179 3168.1
## - gender:lunch_type 1 140.8 72949 3168.3
## - gender:ethnic_group 4 914.4 73723 3168.5
## - parent_educ:is_first_child 5 1171.9 73980 3168.5
## <none> 72808 3169.1
## - test_prep:parent_marital_status 2 532.2 73340 3169.4
## - lunch_type:transport_means 1 287.4 73096 3169.4
## - is_first_child:wkly_study_hours 2 545.4 73354 3169.5
## - ethnic_group:parent_marital_status 9 2363.0 75171 3170.0
## - ethnic_group:transport_means 4 1190.2 73998 3170.7
## - practice_sport:transport_means 2 751.2 73559 3171.2
## - is_first_child:transport_means 1 510.9 73319 3171.2
## - test_prep:wkly_study_hours 2 786.4 73595 3171.5
## - lunch_type:practice_sport 2 835.6 73644 3171.9
## - parent_educ:practice_sport 10 2882.8 75691 3172.0
## - parent_marital_status:transport_means 3 1345.6 74154 3173.9
## - ethnic_group:is_first_child 4 1656.4 74465 3174.4
## - parent_marital_status:wkly_study_hours 4 1675.9 74484 3174.5
## - parent_educ:parent_marital_status 13 4184.5 76993 3176.1
## + parent_educ:lunch_type 5 294.6 72514 3176.7
## + ethnic_group:wkly_study_hours 8 1025.2 71783 3176.8
## + parent_educ:wkly_study_hours 10 1298.6 71510 3178.5
## - parent_marital_status:is_first_child 2 1962.0 74770 3180.8
## + ethnic_group:parent_educ 20 2526.6 70282 3188.3
##
## Step: AIC=3162.03
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:practice_sport 8 1278.6 74446 3156.2
## - gender:parent_marital_status 3 87.6 73255 3156.7
## - parent_marital_status:practice_sport 4 490.9 73659 3158.0
## - ethnic_group:test_prep 4 630.4 73798 3159.1
## - test_prep:practice_sport 2 132.4 73300 3159.1
## - gender:wkly_study_hours 2 150.1 73318 3159.2
## - ethnic_group:lunch_type 4 667.4 73835 3159.4
## - parent_educ:transport_means 5 964.9 74132 3159.8
## - gender:practice_sport 2 214.9 73382 3159.8
## - gender:transport_means 1 0.1 73168 3160.0
## - gender:parent_educ 5 1000.6 74168 3160.0
## - practice_sport:wkly_study_hours 4 751.8 73919 3160.1
## - lunch_type:test_prep 1 7.1 73175 3160.1
## - test_prep:transport_means 1 12.8 73180 3160.1
## - transport_means:wkly_study_hours 2 262.3 73430 3160.1
## - lunch_type:is_first_child 1 24.2 73192 3160.2
## - gender:is_first_child 1 25.1 73193 3160.2
## - practice_sport:is_first_child 2 277.1 73445 3160.3
## - test_prep:is_first_child 1 46.8 73214 3160.4
## - gender:test_prep 1 47.0 73215 3160.4
## - lunch_type:parent_marital_status 2 304.2 73472 3160.5
## - gender:lunch_type 1 121.5 73289 3161.0
## - lunch_type:wkly_study_hours 2 410.5 73578 3161.3
## - gender:ethnic_group 4 912.8 74080 3161.3
## - parent_educ:is_first_child 5 1196.4 74364 3161.6
## - is_first_child:wkly_study_hours 2 486.7 73654 3161.9
## <none> 73168 3162.0
## - lunch_type:transport_means 1 256.3 73424 3162.1
## - test_prep:parent_marital_status 2 519.3 73687 3162.2
## - ethnic_group:parent_marital_status 9 2307.6 75475 3162.3
## - ethnic_group:transport_means 4 1145.8 74313 3163.2
## - practice_sport:transport_means 2 780.1 73948 3164.3
## - parent_educ:practice_sport 10 2851.5 76019 3164.6
## - is_first_child:transport_means 1 590.4 73758 3164.8
## - test_prep:wkly_study_hours 2 856.9 74024 3164.9
## - lunch_type:practice_sport 2 894.2 74062 3165.2
## - parent_marital_status:transport_means 3 1347.2 74515 3166.8
## - parent_marital_status:wkly_study_hours 4 1749.0 74917 3168.0
## - ethnic_group:is_first_child 4 1750.8 74918 3168.0
## - parent_educ:parent_marital_status 13 4071.8 77239 3168.0
## + parent_educ:test_prep 5 359.4 72808 3169.1
## + ethnic_group:wkly_study_hours 8 1054.8 72113 3169.5
## + parent_educ:lunch_type 5 228.9 72939 3170.2
## + parent_educ:wkly_study_hours 10 1351.3 71816 3171.0
## - parent_marital_status:is_first_child 2 2006.6 75174 3174.0
## + ethnic_group:parent_educ 20 2379.5 70788 3182.5
##
## Step: AIC=3156.25
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 67.0 74513 3150.8
## - parent_educ:transport_means 5 841.7 75288 3152.9
## - test_prep:practice_sport 2 106.9 74553 3153.1
## - ethnic_group:test_prep 4 620.2 75066 3153.1
## - gender:parent_educ 5 928.1 75374 3153.6
## - parent_marital_status:practice_sport 4 715.9 75162 3153.9
## - gender:ethnic_group 4 740.0 75186 3154.1
## - practice_sport:is_first_child 2 233.2 74679 3154.1
## - gender:wkly_study_hours 2 239.5 74686 3154.1
## - ethnic_group:lunch_type 4 753.4 75200 3154.2
## - practice_sport:wkly_study_hours 4 757.6 75204 3154.2
## - gender:transport_means 1 0.0 74446 3154.2
## - gender:is_first_child 1 4.0 74450 3154.3
## - lunch_type:is_first_child 1 6.3 74452 3154.3
## - test_prep:transport_means 1 14.3 74461 3154.4
## - gender:test_prep 1 27.0 74473 3154.5
## - test_prep:is_first_child 1 36.1 74482 3154.5
## - lunch_type:test_prep 1 40.4 74487 3154.6
## - transport_means:wkly_study_hours 2 312.2 74758 3154.7
## - lunch_type:parent_marital_status 2 336.7 74783 3154.9
## - gender:lunch_type 1 91.8 74538 3155.0
## - gender:practice_sport 2 372.3 74818 3155.2
## - lunch_type:wkly_study_hours 2 438.7 74885 3155.7
## - lunch_type:transport_means 1 207.5 74654 3155.9
## <none> 74446 3156.2
## - is_first_child:wkly_study_hours 2 513.1 74959 3156.3
## - test_prep:parent_marital_status 2 564.5 75011 3156.7
## - ethnic_group:parent_marital_status 9 2399.2 76845 3157.0
## - parent_educ:is_first_child 5 1373.5 75820 3157.0
## - test_prep:wkly_study_hours 2 686.9 75133 3157.7
## - ethnic_group:transport_means 4 1209.0 75655 3157.8
## - practice_sport:transport_means 2 767.5 75214 3158.3
## - lunch_type:practice_sport 2 901.2 75347 3159.3
## - parent_educ:practice_sport 10 2985.5 77432 3159.4
## - is_first_child:transport_means 1 699.2 75145 3159.8
## - ethnic_group:is_first_child 4 1570.1 76016 3160.6
## - parent_educ:parent_marital_status 13 4000.5 78447 3161.1
## - parent_marital_status:transport_means 3 1482.2 75928 3161.9
## + ethnic_group:practice_sport 8 1278.6 73168 3162.0
## - parent_marital_status:wkly_study_hours 4 1838.7 76285 3162.6
## + parent_educ:test_prep 5 350.9 74095 3163.5
## + ethnic_group:wkly_study_hours 8 1066.6 73380 3163.7
## + parent_educ:lunch_type 5 190.6 74256 3164.7
## + parent_educ:wkly_study_hours 10 1298.4 73148 3165.9
## - parent_marital_status:is_first_child 2 1757.2 76203 3166.0
## + ethnic_group:parent_educ 20 2053.9 72392 3179.7
##
## Step: AIC=3150.78
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:transport_means 5 837.2 75350 3147.4
## - test_prep:practice_sport 2 123.5 74637 3147.8
## - ethnic_group:test_prep 4 647.9 75161 3147.9
## - gender:parent_educ 5 953.7 75467 3148.3
## - parent_marital_status:practice_sport 4 707.6 75221 3148.4
## - gender:ethnic_group 4 713.3 75227 3148.4
## - practice_sport:is_first_child 2 226.7 74740 3148.6
## - gender:transport_means 1 0.1 74513 3148.8
## - ethnic_group:lunch_type 4 763.7 75277 3148.8
## - lunch_type:is_first_child 1 5.5 74519 3148.8
## - gender:wkly_study_hours 2 259.9 74773 3148.8
## - gender:is_first_child 1 7.7 74521 3148.8
## - test_prep:transport_means 1 13.5 74527 3148.9
## - practice_sport:wkly_study_hours 4 781.9 75295 3148.9
## - gender:test_prep 1 30.2 74543 3149.0
## - test_prep:is_first_child 1 37.1 74550 3149.1
## - lunch_type:test_prep 1 38.2 74551 3149.1
## - transport_means:wkly_study_hours 2 313.8 74827 3149.3
## - gender:lunch_type 1 86.4 74600 3149.5
## - lunch_type:parent_marital_status 2 372.7 74886 3149.7
## - gender:practice_sport 2 398.1 74911 3149.9
## - lunch_type:wkly_study_hours 2 465.2 74978 3150.5
## - lunch_type:transport_means 1 219.7 74733 3150.5
## - is_first_child:wkly_study_hours 2 502.1 75015 3150.7
## <none> 74513 3150.8
## - test_prep:parent_marital_status 2 572.4 75086 3151.3
## - parent_educ:is_first_child 5 1383.9 75897 3151.6
## - test_prep:wkly_study_hours 2 682.1 75195 3152.2
## - ethnic_group:transport_means 4 1201.4 75715 3152.2
## - practice_sport:transport_means 2 757.6 75271 3152.7
## - ethnic_group:parent_marital_status 9 2645.4 77159 3153.4
## - lunch_type:practice_sport 2 979.2 75492 3154.5
## - parent_educ:practice_sport 10 3086.3 77599 3154.7
## - is_first_child:transport_means 1 756.1 75269 3154.7
## - ethnic_group:is_first_child 4 1552.8 76066 3154.9
## - parent_educ:parent_marital_status 13 3992.8 78506 3155.6
## + gender:parent_marital_status 3 67.0 74446 3156.2
## + ethnic_group:practice_sport 8 1258.0 73255 3156.7
## - parent_marital_status:wkly_study_hours 4 1820.1 76333 3157.0
## - parent_marital_status:transport_means 3 1677.8 76191 3157.9
## + parent_educ:test_prep 5 353.8 74159 3158.0
## + ethnic_group:wkly_study_hours 8 1069.4 73444 3158.3
## + parent_educ:lunch_type 5 197.6 74316 3159.2
## + parent_educ:wkly_study_hours 10 1285.8 73227 3160.5
## - parent_marital_status:is_first_child 2 1819.2 76332 3161.0
## + ethnic_group:parent_educ 20 2094.0 72419 3174.0
##
## Step: AIC=3147.37
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:ethnic_group 4 625.0 75975 3144.2
## - parent_marital_status:practice_sport 4 639.9 75990 3144.4
## - test_prep:practice_sport 2 137.2 75488 3144.4
## - practice_sport:is_first_child 2 183.7 75534 3144.8
## - ethnic_group:test_prep 4 699.4 76050 3144.8
## - gender:parent_educ 5 964.7 76315 3144.9
## - gender:wkly_study_hours 2 223.3 75574 3145.1
## - gender:transport_means 1 0.0 75350 3145.4
## - lunch_type:is_first_child 1 3.2 75354 3145.4
## - gender:is_first_child 1 3.4 75354 3145.4
## - test_prep:transport_means 1 18.3 75369 3145.5
## - gender:test_prep 1 25.6 75376 3145.6
## - transport_means:wkly_study_hours 2 288.2 75639 3145.6
## - lunch_type:test_prep 1 45.2 75396 3145.7
## - test_prep:is_first_child 1 70.8 75421 3145.9
## - practice_sport:wkly_study_hours 4 851.2 76202 3146.0
## - gender:lunch_type 1 110.4 75461 3146.2
## - ethnic_group:lunch_type 4 903.0 76253 3146.4
## - lunch_type:parent_marital_status 2 449.3 75800 3146.9
## - is_first_child:wkly_study_hours 2 475.6 75826 3147.1
## - lunch_type:transport_means 1 226.7 75577 3147.1
## - gender:practice_sport 2 488.4 75839 3147.2
## <none> 75350 3147.4
## - test_prep:parent_marital_status 2 561.5 75912 3147.8
## - lunch_type:wkly_study_hours 2 588.6 75939 3148.0
## - practice_sport:transport_means 2 593.3 75944 3148.0
## - parent_educ:is_first_child 5 1426.3 76777 3148.4
## - test_prep:wkly_study_hours 2 674.7 76025 3148.6
## - ethnic_group:transport_means 4 1321.3 76672 3149.6
## - ethnic_group:parent_marital_status 9 2697.0 78047 3150.1
## - parent_educ:practice_sport 10 3037.1 78388 3150.7
## - is_first_child:transport_means 1 689.2 76040 3150.7
## + parent_educ:transport_means 5 837.2 74513 3150.8
## - ethnic_group:is_first_child 4 1647.5 76998 3152.1
## - lunch_type:practice_sport 2 1148.9 76499 3152.3
## - parent_educ:parent_marital_status 13 4056.5 79407 3152.3
## + gender:parent_marital_status 3 62.5 75288 3152.9
## - parent_marital_status:transport_means 3 1562.5 76913 3153.5
## - parent_marital_status:wkly_study_hours 4 1918.6 77269 3154.2
## + parent_educ:test_prep 5 390.5 74960 3154.3
## + ethnic_group:practice_sport 8 1138.4 74212 3154.4
## + parent_educ:lunch_type 5 246.2 75104 3155.4
## + ethnic_group:wkly_study_hours 8 977.8 74373 3155.7
## - parent_marital_status:is_first_child 2 1802.2 77153 3157.3
## + parent_educ:wkly_study_hours 10 1256.7 74094 3157.4
## + ethnic_group:parent_educ 20 2385.2 72965 3168.4
##
## Step: AIC=3144.24
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:parent_educ +
## gender:lunch_type + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_educ 5 803.3 76779 3140.5
## - ethnic_group:test_prep 4 583.4 76559 3140.8
## - parent_marital_status:practice_sport 4 607.7 76583 3140.9
## - test_prep:practice_sport 2 130.4 76106 3141.3
## - practice_sport:is_first_child 2 230.6 76206 3142.0
## - gender:transport_means 1 2.2 75978 3142.3
## - lunch_type:is_first_child 1 2.4 75978 3142.3
## - gender:is_first_child 1 8.7 75984 3142.3
## - gender:test_prep 1 14.5 75990 3142.4
## - test_prep:transport_means 1 15.5 75991 3142.4
## - gender:wkly_study_hours 2 283.2 76259 3142.4
## - lunch_type:test_prep 1 62.2 76038 3142.7
## - transport_means:wkly_study_hours 2 331.5 76307 3142.8
## - test_prep:is_first_child 1 78.2 76054 3142.9
## - gender:lunch_type 1 98.6 76074 3143.0
## - practice_sport:wkly_study_hours 4 895.9 76871 3143.2
## - ethnic_group:lunch_type 4 898.8 76874 3143.2
## - lunch_type:parent_marital_status 2 387.7 76363 3143.2
## - is_first_child:wkly_study_hours 2 485.3 76461 3144.0
## - lunch_type:transport_means 1 230.9 76206 3144.0
## - gender:practice_sport 2 505.5 76481 3144.2
## <none> 75975 3144.2
## - test_prep:parent_marital_status 2 573.9 76549 3144.7
## - lunch_type:wkly_study_hours 2 580.0 76555 3144.7
## - practice_sport:transport_means 2 587.3 76563 3144.8
## - test_prep:wkly_study_hours 2 723.8 76699 3145.8
## - ethnic_group:parent_marital_status 9 2606.7 78582 3146.1
## - ethnic_group:transport_means 4 1335.3 77311 3146.5
## - parent_educ:is_first_child 5 1638.2 77614 3146.8
## + gender:ethnic_group 4 625.0 75350 3147.4
## - parent_educ:practice_sport 10 3044.3 79020 3147.4
## - is_first_child:transport_means 1 745.1 76720 3148.0
## + parent_educ:transport_means 5 748.8 75227 3148.4
## - ethnic_group:is_first_child 4 1618.4 77594 3148.7
## - parent_educ:parent_marital_status 13 4147.5 80123 3149.6
## + gender:parent_marital_status 3 53.1 75922 3149.8
## - parent_marital_status:wkly_study_hours 4 1869.3 77845 3150.6
## - lunch_type:practice_sport 2 1362.2 77338 3150.7
## - parent_marital_status:transport_means 3 1625.8 77601 3150.7
## + parent_educ:test_prep 5 378.4 75597 3151.3
## + parent_educ:lunch_type 5 249.3 75726 3152.3
## + ethnic_group:practice_sport 8 990.4 74985 3152.5
## + ethnic_group:wkly_study_hours 8 951.0 75024 3152.8
## + parent_educ:wkly_study_hours 10 1276.1 74699 3154.3
## - parent_marital_status:is_first_child 2 1937.3 77913 3155.1
## + ethnic_group:parent_educ 20 2426.2 73549 3165.1
##
## Step: AIC=3140.45
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:test_prep 4 579.8 77359 3136.9
## - parent_marital_status:practice_sport 4 610.1 77389 3137.1
## - test_prep:practice_sport 2 174.1 76953 3137.8
## - gender:transport_means 1 2.3 76781 3138.5
## - lunch_type:is_first_child 1 3.9 76783 3138.5
## - gender:is_first_child 1 8.2 76787 3138.5
## - ethnic_group:lunch_type 4 793.2 77572 3138.5
## - test_prep:transport_means 1 8.6 76787 3138.5
## - practice_sport:is_first_child 2 271.5 77050 3138.5
## - gender:test_prep 1 13.6 76792 3138.6
## - gender:wkly_study_hours 2 305.8 77084 3138.8
## - transport_means:wkly_study_hours 2 333.7 77112 3139.0
## - practice_sport:wkly_study_hours 4 866.5 77645 3139.1
## - lunch_type:test_prep 1 89.9 76869 3139.1
## - lunch_type:parent_marital_status 2 356.6 77135 3139.2
## - gender:lunch_type 1 106.1 76885 3139.3
## - test_prep:is_first_child 1 121.6 76900 3139.4
## - gender:practice_sport 2 513.8 77292 3140.4
## <none> 76779 3140.4
## - test_prep:parent_marital_status 2 543.9 77323 3140.6
## - is_first_child:wkly_study_hours 2 547.5 77326 3140.6
## - practice_sport:transport_means 2 576.1 77355 3140.9
## - lunch_type:transport_means 1 337.5 77116 3141.0
## - lunch_type:wkly_study_hours 2 602.4 77381 3141.1
## - ethnic_group:parent_marital_status 9 2495.1 79274 3141.3
## - parent_educ:is_first_child 5 1473.0 78252 3141.7
## - test_prep:wkly_study_hours 2 793.8 77573 3142.5
## - parent_educ:practice_sport 10 2997.2 79776 3143.0
## - ethnic_group:transport_means 4 1487.1 78266 3143.8
## - is_first_child:transport_means 1 729.0 77508 3144.0
## + gender:parent_educ 5 803.3 75975 3144.2
## - ethnic_group:is_first_child 4 1574.1 78353 3144.4
## + parent_educ:transport_means 5 771.5 76007 3144.5
## + gender:ethnic_group 4 463.6 76315 3144.9
## + gender:parent_marital_status 3 49.7 76729 3146.1
## - lunch_type:practice_sport 2 1378.5 78157 3146.9
## - parent_marital_status:wkly_study_hours 4 1932.2 78711 3147.1
## - parent_marital_status:transport_means 3 1712.3 78491 3147.5
## + parent_educ:test_prep 5 325.1 76454 3147.9
## + parent_educ:lunch_type 5 253.8 76525 3148.5
## - parent_educ:parent_marital_status 13 4591.9 81371 3148.7
## + ethnic_group:practice_sport 8 953.6 75825 3149.1
## + ethnic_group:wkly_study_hours 8 934.0 75845 3149.2
## + parent_educ:wkly_study_hours 10 1262.9 75516 3150.7
## - parent_marital_status:is_first_child 2 1915.9 78695 3151.0
## + ethnic_group:parent_educ 20 2444.2 74335 3161.4
##
## Step: AIC=3136.89
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:practice_sport 4 533.2 77892 3132.9
## - test_prep:practice_sport 2 161.1 77520 3134.1
## - ethnic_group:lunch_type 4 747.4 78106 3134.6
## - gender:transport_means 1 1.4 77360 3134.9
## - gender:is_first_child 1 3.8 77362 3134.9
## - lunch_type:is_first_child 1 8.7 77367 3135.0
## - gender:test_prep 1 10.2 77369 3135.0
## - test_prep:transport_means 1 11.0 77370 3135.0
## - gender:wkly_study_hours 2 274.9 77633 3135.0
## - practice_sport:is_first_child 2 307.1 77666 3135.2
## - practice_sport:wkly_study_hours 4 846.0 78204 3135.3
## - transport_means:wkly_study_hours 2 321.1 77680 3135.3
## - lunch_type:test_prep 1 90.8 77449 3135.6
## - lunch_type:parent_marital_status 2 359.1 77718 3135.6
## - gender:lunch_type 1 96.6 77455 3135.6
## - test_prep:is_first_child 1 102.3 77461 3135.7
## - test_prep:parent_marital_status 2 465.8 77824 3136.4
## - gender:practice_sport 2 500.6 77859 3136.7
## - is_first_child:wkly_study_hours 2 507.8 77866 3136.8
## <none> 77359 3136.9
## - ethnic_group:parent_marital_status 9 2421.8 79780 3137.1
## - practice_sport:transport_means 2 583.7 77942 3137.3
## - lunch_type:transport_means 1 352.8 77711 3137.6
## - lunch_type:wkly_study_hours 2 639.5 77998 3137.8
## - parent_educ:is_first_child 5 1498.7 78857 3138.2
## - parent_educ:practice_sport 10 3002.3 80361 3139.3
## - test_prep:wkly_study_hours 2 860.1 78219 3139.4
## - is_first_child:transport_means 1 727.5 78086 3140.4
## + ethnic_group:test_prep 4 579.8 76779 3140.4
## + parent_educ:transport_means 5 819.8 76539 3140.6
## + gender:parent_educ 5 799.7 76559 3140.8
## - ethnic_group:is_first_child 4 1599.6 78958 3141.0
## - ethnic_group:transport_means 4 1611.9 78970 3141.1
## + gender:ethnic_group 4 374.8 76984 3142.0
## + gender:parent_marital_status 3 72.6 77286 3142.3
## - parent_marital_status:wkly_study_hours 4 1929.3 79288 3143.4
## - lunch_type:practice_sport 2 1417.0 78776 3143.6
## - parent_marital_status:transport_means 3 1711.0 79070 3143.8
## + parent_educ:test_prep 5 315.5 77043 3144.5
## + parent_educ:lunch_type 5 243.5 77115 3145.0
## - parent_educ:parent_marital_status 13 4692.5 82051 3145.6
## + ethnic_group:practice_sport 8 942.1 76416 3145.7
## + ethnic_group:wkly_study_hours 8 878.6 76480 3146.2
## + parent_educ:wkly_study_hours 10 1190.6 76168 3147.7
## - parent_marital_status:is_first_child 2 2031.7 79390 3148.2
## + ethnic_group:parent_educ 20 2464.6 74894 3157.8
##
## Step: AIC=3132.94
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:parent_marital_status 3 368.2 78260 3129.7
## - test_prep:practice_sport 2 150.3 78042 3130.1
## - ethnic_group:lunch_type 4 775.5 78667 3130.8
## - practice_sport:is_first_child 2 265.2 78157 3130.9
## - gender:is_first_child 1 1.6 77893 3130.9
## - gender:transport_means 1 3.6 77895 3131.0
## - test_prep:transport_means 1 9.1 77901 3131.0
## - lunch_type:is_first_child 1 14.4 77906 3131.1
## - gender:test_prep 1 22.0 77914 3131.1
## - gender:wkly_study_hours 2 316.5 78208 3131.3
## - transport_means:wkly_study_hours 2 323.4 78215 3131.4
## - ethnic_group:parent_marital_status 10 2477.6 80369 3131.4
## - practice_sport:wkly_study_hours 4 878.9 78771 3131.6
## - test_prep:is_first_child 1 96.0 77988 3131.7
## - lunch_type:test_prep 1 100.7 77992 3131.7
## - gender:lunch_type 1 110.2 78002 3131.8
## - test_prep:parent_marital_status 2 413.7 78305 3132.1
## - is_first_child:wkly_study_hours 2 514.9 78407 3132.8
## - gender:practice_sport 2 523.4 78415 3132.9
## <none> 77892 3132.9
## - practice_sport:transport_means 2 544.8 78437 3133.1
## - lunch_type:transport_means 1 315.9 78208 3133.3
## - lunch_type:wkly_study_hours 2 646.8 78539 3133.8
## - parent_educ:is_first_child 5 1450.7 79342 3133.8
## - parent_educ:practice_sport 10 2867.2 80759 3134.3
## - ethnic_group:transport_means 4 1416.9 79309 3135.6
## - test_prep:wkly_study_hours 2 963.4 78855 3136.2
## - is_first_child:transport_means 1 722.5 78614 3136.4
## + parent_marital_status:practice_sport 4 533.2 77359 3136.9
## + gender:parent_educ 5 794.5 77097 3136.9
## - ethnic_group:is_first_child 4 1601.7 79493 3136.9
## + parent_educ:transport_means 5 772.0 77120 3137.1
## + ethnic_group:test_prep 4 502.9 77389 3137.1
## - parent_marital_status:wkly_study_hours 5 1966.9 79859 3137.7
## + gender:ethnic_group 4 347.9 77544 3138.3
## + gender:parent_marital_status 3 64.2 77828 3138.5
## - parent_marital_status:transport_means 3 1696.1 79588 3139.7
## - lunch_type:practice_sport 2 1453.7 79345 3139.8
## + parent_educ:test_prep 5 317.5 77574 3140.5
## + ethnic_group:practice_sport 8 1088.4 76803 3140.6
## + parent_educ:lunch_type 5 251.8 77640 3141.0
## + ethnic_group:wkly_study_hours 8 797.6 77094 3142.9
## - parent_educ:parent_marital_status 14 5190.5 83082 3143.0
## + parent_educ:wkly_study_hours 10 1174.0 76718 3144.0
## - parent_marital_status:is_first_child 2 2196.3 80088 3145.3
## + ethnic_group:parent_educ 20 2483.8 75408 3153.8
##
## Step: AIC=3129.72
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 165.1 78425 3127.0
## - practice_sport:is_first_child 2 212.2 78472 3127.3
## - ethnic_group:lunch_type 4 777.4 79037 3127.6
## - gender:is_first_child 1 4.9 78265 3127.8
## - gender:wkly_study_hours 2 271.6 78532 3127.8
## - gender:transport_means 1 6.8 78267 3127.8
## - test_prep:transport_means 1 10.2 78270 3127.8
## - ethnic_group:parent_marital_status 10 2435.5 80696 3127.8
## - lunch_type:is_first_child 1 18.4 78278 3127.9
## - practice_sport:wkly_study_hours 4 826.1 79086 3127.9
## - gender:test_prep 1 38.7 78299 3128.0
## - lunch_type:test_prep 1 84.5 78345 3128.4
## - test_prep:is_first_child 1 94.7 78355 3128.4
## - transport_means:wkly_study_hours 2 361.1 78621 3128.4
## - test_prep:parent_marital_status 2 404.9 78665 3128.8
## - gender:lunch_type 1 155.7 78416 3128.9
## - gender:practice_sport 2 481.8 78742 3129.3
## - is_first_child:wkly_study_hours 2 484.9 78745 3129.4
## <none> 78260 3129.7
## - practice_sport:transport_means 2 535.6 78796 3129.8
## - lunch_type:transport_means 1 321.4 78581 3130.1
## - parent_educ:is_first_child 5 1397.5 79657 3130.2
## - lunch_type:wkly_study_hours 2 592.2 78852 3130.2
## - parent_educ:practice_sport 10 2842.9 81103 3130.8
## - ethnic_group:transport_means 4 1371.7 79632 3132.0
## - test_prep:wkly_study_hours 2 944.1 79204 3132.8
## + lunch_type:parent_marital_status 3 368.2 77892 3132.9
## - is_first_child:transport_means 1 745.6 79006 3133.3
## + parent_educ:transport_means 5 837.1 77423 3133.4
## - ethnic_group:is_first_child 4 1603.9 79864 3133.7
## + ethnic_group:test_prep 4 514.1 77746 3133.8
## + gender:parent_educ 5 758.5 77501 3134.0
## - parent_marital_status:wkly_study_hours 5 1918.3 80178 3134.0
## + gender:parent_marital_status 3 93.8 78166 3135.0
## + gender:ethnic_group 4 302.8 77957 3135.4
## + parent_marital_status:practice_sport 5 542.4 77718 3135.6
## - lunch_type:practice_sport 2 1379.3 79639 3136.0
## - parent_marital_status:transport_means 3 1664.3 79924 3136.1
## + parent_educ:test_prep 5 319.0 77941 3137.3
## + ethnic_group:practice_sport 8 1103.5 77156 3137.3
## + parent_educ:lunch_type 5 272.2 77988 3137.7
## + ethnic_group:wkly_study_hours 8 800.2 77460 3139.7
## + parent_educ:wkly_study_hours 10 1154.0 77106 3141.0
## - parent_marital_status:is_first_child 2 2180.7 80441 3141.9
## - parent_educ:parent_marital_status 14 5685.1 83945 3143.1
## + ethnic_group:parent_educ 20 2274.4 75986 3152.3
##
## Step: AIC=3126.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_marital_status 10 2362.3 80787 3124.5
## - practice_sport:is_first_child 2 234.6 78660 3124.7
## - gender:wkly_study_hours 2 257.8 78683 3124.9
## - gender:is_first_child 1 2.9 78428 3125.0
## - gender:transport_means 1 6.5 78432 3125.0
## - test_prep:transport_means 1 14.0 78439 3125.1
## - lunch_type:is_first_child 1 17.1 78442 3125.1
## - ethnic_group:lunch_type 4 837.1 79262 3125.2
## - gender:test_prep 1 37.2 78462 3125.2
## - practice_sport:wkly_study_hours 4 865.2 79290 3125.4
## - lunch_type:test_prep 1 92.0 78517 3125.7
## - test_prep:is_first_child 1 99.3 78524 3125.7
## - transport_means:wkly_study_hours 2 387.2 78812 3125.9
## - gender:lunch_type 1 168.8 78594 3126.2
## - test_prep:parent_marital_status 2 444.0 78869 3126.3
## - is_first_child:wkly_study_hours 2 453.2 78878 3126.4
## - practice_sport:transport_means 2 506.4 78931 3126.8
## - gender:practice_sport 2 509.9 78935 3126.8
## <none> 78425 3127.0
## - lunch_type:transport_means 1 319.5 78745 3127.4
## - lunch_type:wkly_study_hours 2 643.8 79069 3127.8
## - parent_educ:practice_sport 10 2891.2 81316 3128.3
## - parent_educ:is_first_child 5 1540.6 79966 3128.4
## - ethnic_group:transport_means 4 1350.2 79775 3129.0
## + test_prep:practice_sport 2 165.1 78260 3129.7
## + lunch_type:parent_marital_status 3 383.1 78042 3130.1
## - test_prep:wkly_study_hours 2 952.3 79377 3130.1
## + parent_educ:transport_means 5 852.2 77573 3130.5
## - is_first_child:transport_means 1 755.8 79181 3130.6
## + gender:parent_educ 5 805.0 77620 3130.9
## - parent_marital_status:wkly_study_hours 5 1874.3 80299 3130.9
## - ethnic_group:is_first_child 4 1614.4 80040 3131.0
## + ethnic_group:test_prep 4 497.3 77928 3131.2
## + gender:parent_marital_status 3 119.3 78306 3132.1
## + gender:ethnic_group 4 285.5 78140 3132.8
## + parent_marital_status:practice_sport 5 529.7 77895 3133.0
## - parent_marital_status:transport_means 3 1654.2 80079 3133.3
## - lunch_type:practice_sport 2 1438.7 79864 3133.7
## + parent_educ:test_prep 5 295.7 78129 3134.7
## + ethnic_group:practice_sport 8 1085.0 77340 3134.8
## + parent_educ:lunch_type 5 267.4 78158 3134.9
## + ethnic_group:wkly_study_hours 8 780.9 77644 3137.1
## + parent_educ:wkly_study_hours 10 1191.5 77234 3137.9
## - parent_marital_status:is_first_child 2 2135.4 80561 3138.8
## - parent_educ:parent_marital_status 14 5615.3 84040 3139.8
## + ethnic_group:parent_educ 20 2354.4 76071 3149.0
##
## Step: AIC=3124.48
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:is_first_child 2 134.9 80922 3121.5
## - practice_sport:wkly_study_hours 4 706.5 81494 3121.6
## - gender:wkly_study_hours 2 192.1 80980 3121.9
## - transport_means:wkly_study_hours 2 268.3 81056 3122.4
## - practice_sport:transport_means 2 270.0 81057 3122.4
## - test_prep:parent_marital_status 3 558.2 81346 3122.5
## - test_prep:transport_means 1 12.1 80800 3122.6
## - gender:is_first_child 1 21.6 80809 3122.6
## - gender:transport_means 1 26.2 80814 3122.7
## - lunch_type:is_first_child 1 35.8 80823 3122.7
## - ethnic_group:lunch_type 4 873.8 81661 3122.8
## - parent_educ:practice_sport 10 2583.4 83371 3123.1
## - lunch_type:test_prep 1 87.2 80875 3123.1
## - gender:test_prep 1 91.6 80879 3123.2
## - test_prep:is_first_child 1 138.6 80926 3123.5
## - is_first_child:wkly_study_hours 2 434.4 81222 3123.6
## - gender:lunch_type 1 177.5 80965 3123.8
## - gender:practice_sport 2 524.9 81312 3124.3
## <none> 80787 3124.5
## - lunch_type:wkly_study_hours 2 609.6 81397 3124.9
## - parent_marital_status:wkly_study_hours 6 1735.4 82523 3125.0
## - lunch_type:transport_means 1 384.1 81172 3125.3
## - ethnic_group:is_first_child 4 1283.6 82071 3125.8
## - ethnic_group:transport_means 4 1329.1 82117 3126.1
## - parent_educ:is_first_child 5 1623.5 82411 3126.2
## + ethnic_group:parent_marital_status 10 2362.3 78425 3127.0
## + gender:parent_marital_status 3 436.1 80351 3127.3
## - parent_marital_status:transport_means 3 1233.0 82020 3127.4
## + parent_educ:transport_means 5 917.7 79870 3127.7
## + test_prep:practice_sport 2 91.9 80696 3127.8
## + lunch_type:parent_marital_status 3 338.3 80449 3128.0
## - test_prep:wkly_study_hours 2 1155.0 81942 3128.8
## + ethnic_group:test_prep 4 446.8 80341 3129.2
## + gender:parent_educ 5 707.0 80080 3129.3
## - is_first_child:transport_means 1 981.3 81769 3129.6
## + gender:ethnic_group 4 243.7 80544 3130.7
## + parent_marital_status:practice_sport 6 627.4 80160 3131.9
## - lunch_type:practice_sport 2 1582.8 82370 3131.9
## + parent_educ:test_prep 5 304.0 80483 3132.2
## + parent_educ:lunch_type 5 266.7 80521 3132.5
## + ethnic_group:practice_sport 8 1071.0 79716 3132.6
## - parent_marital_status:is_first_child 3 2014.8 82802 3133.0
## - parent_educ:parent_marital_status 15 5583.0 86370 3133.9
## + parent_educ:wkly_study_hours 10 1312.1 79475 3134.8
## + ethnic_group:wkly_study_hours 8 702.7 80085 3135.3
## + ethnic_group:parent_educ 20 2394.3 78393 3146.7
##
## Step: AIC=3121.46
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 746.1 81668 3118.9
## - gender:wkly_study_hours 2 197.4 81120 3118.9
## - practice_sport:transport_means 2 256.1 81178 3119.3
## - test_prep:parent_marital_status 3 542.8 81465 3119.4
## - transport_means:wkly_study_hours 2 274.7 81197 3119.5
## - test_prep:transport_means 1 12.3 80935 3119.6
## - gender:is_first_child 1 25.8 80948 3119.7
## - lunch_type:is_first_child 1 27.4 80950 3119.7
## - gender:transport_means 1 32.3 80955 3119.7
## - parent_educ:practice_sport 10 2575.3 83498 3119.9
## - ethnic_group:lunch_type 4 901.1 81823 3120.0
## - lunch_type:test_prep 1 98.2 81021 3120.2
## - gender:test_prep 1 100.2 81023 3120.2
## - test_prep:is_first_child 1 105.9 81028 3120.2
## - is_first_child:wkly_study_hours 2 409.4 81332 3120.4
## - gender:lunch_type 1 186.1 81108 3120.8
## - gender:practice_sport 2 520.7 81443 3121.2
## <none> 80922 3121.5
## - lunch_type:wkly_study_hours 2 614.4 81537 3121.9
## - parent_marital_status:wkly_study_hours 6 1743.9 82666 3122.0
## - lunch_type:transport_means 1 376.8 81299 3122.2
## - ethnic_group:transport_means 4 1280.0 82202 3122.7
## - parent_educ:is_first_child 5 1598.0 82520 3123.0
## - ethnic_group:is_first_child 4 1368.9 82291 3123.4
## - parent_marital_status:transport_means 3 1178.7 82101 3124.0
## + gender:parent_marital_status 3 414.4 80508 3124.4
## + practice_sport:is_first_child 2 134.9 80787 3124.5
## + test_prep:practice_sport 2 104.1 80818 3124.7
## + ethnic_group:parent_marital_status 10 2262.6 78660 3124.7
## + parent_educ:transport_means 5 873.3 80049 3125.1
## + lunch_type:parent_marital_status 3 286.4 80636 3125.4
## - test_prep:wkly_study_hours 2 1121.2 82044 3125.6
## + ethnic_group:test_prep 4 475.9 80446 3126.0
## + gender:parent_educ 5 724.6 80198 3126.2
## - is_first_child:transport_means 1 1054.5 81977 3127.1
## + gender:ethnic_group 4 280.3 80642 3127.4
## - lunch_type:practice_sport 2 1568.5 82491 3128.8
## + parent_educ:test_prep 5 352.1 80570 3128.9
## + parent_educ:lunch_type 5 272.5 80650 3129.5
## + parent_marital_status:practice_sport 6 543.3 80379 3129.5
## - parent_marital_status:is_first_child 3 1952.1 82874 3129.5
## + ethnic_group:practice_sport 8 1035.2 79887 3129.9
## - parent_educ:parent_marital_status 15 5525.4 86448 3130.4
## + parent_educ:wkly_study_hours 10 1304.2 79618 3131.9
## + ethnic_group:wkly_study_hours 8 727.5 80195 3132.1
## + ethnic_group:parent_educ 20 2361.2 78561 3144.0
##
## Step: AIC=3118.88
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:wkly_study_hours 2 179.7 81848 3116.2
## - practice_sport:transport_means 2 229.3 81898 3116.5
## - ethnic_group:lunch_type 4 793.3 82462 3116.6
## - test_prep:parent_marital_status 3 560.0 82228 3116.9
## - test_prep:transport_means 1 11.3 81680 3117.0
## - gender:transport_means 1 15.7 81684 3117.0
## - transport_means:wkly_study_hours 2 295.9 81964 3117.0
## - parent_educ:practice_sport 10 2564.2 84233 3117.1
## - gender:is_first_child 1 44.9 81713 3117.2
## - lunch_type:is_first_child 1 69.4 81738 3117.4
## - gender:test_prep 1 88.2 81757 3117.5
## - lunch_type:test_prep 1 131.6 81800 3117.8
## - test_prep:is_first_child 1 135.8 81804 3117.9
## - gender:lunch_type 1 202.3 81871 3118.3
## - is_first_child:wkly_study_hours 2 498.4 82167 3118.5
## <none> 81668 3118.9
## - lunch_type:wkly_study_hours 2 556.9 82225 3118.9
## - gender:practice_sport 2 560.6 82229 3118.9
## - lunch_type:transport_means 1 336.4 82005 3119.3
## - parent_educ:is_first_child 5 1501.0 83169 3119.6
## - parent_marital_status:wkly_study_hours 6 1807.4 83476 3119.8
## - ethnic_group:transport_means 4 1251.4 82920 3119.8
## - ethnic_group:is_first_child 4 1415.5 83084 3121.0
## + practice_sport:wkly_study_hours 4 746.1 80922 3121.5
## + practice_sport:is_first_child 2 174.5 81494 3121.6
## - parent_marital_status:transport_means 3 1236.0 82904 3121.7
## + test_prep:practice_sport 2 136.1 81532 3121.9
## + gender:parent_marital_status 3 401.9 81267 3122.0
## + parent_educ:transport_means 5 945.4 80723 3122.0
## + lunch_type:parent_marital_status 3 219.3 81449 3123.3
## - test_prep:wkly_study_hours 2 1185.6 82854 3123.4
## + ethnic_group:test_prep 4 471.0 81197 3123.5
## + ethnic_group:parent_marital_status 10 2103.1 79565 3123.5
## + gender:parent_educ 5 705.1 80963 3123.8
## + gender:ethnic_group 4 333.0 81335 3124.5
## - is_first_child:transport_means 1 1069.1 82737 3124.6
## - lunch_type:practice_sport 2 1506.1 83174 3125.7
## + parent_educ:test_prep 5 375.4 81293 3126.2
## + parent_educ:lunch_type 5 326.2 81342 3126.5
## - parent_educ:parent_marital_status 15 5411.4 87080 3126.7
## - parent_marital_status:is_first_child 3 1942.8 83611 3126.8
## + parent_marital_status:practice_sport 6 469.0 81199 3127.5
## + ethnic_group:practice_sport 8 969.6 80699 3127.8
## + ethnic_group:wkly_study_hours 8 807.6 80861 3129.0
## + parent_educ:wkly_study_hours 10 1140.4 80528 3130.6
## + ethnic_group:parent_educ 20 2482.9 79186 3140.7
##
## Step: AIC=3116.17
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:lunch_type + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:lunch_type 4 791.6 82640 3113.8
## - practice_sport:transport_means 2 245.4 82094 3113.9
## - test_prep:parent_marital_status 3 545.1 82393 3114.1
## - test_prep:transport_means 1 11.0 81859 3114.2
## - transport_means:wkly_study_hours 2 290.0 82138 3114.3
## - gender:transport_means 1 18.5 81867 3114.3
## - parent_educ:practice_sport 10 2558.1 84406 3114.3
## - gender:is_first_child 1 48.8 81897 3114.5
## - lunch_type:is_first_child 1 68.8 81917 3114.7
## - gender:test_prep 1 110.7 81959 3115.0
## - lunch_type:test_prep 1 122.5 81971 3115.1
## - test_prep:is_first_child 1 162.3 82010 3115.3
## - gender:lunch_type 1 171.5 82020 3115.4
## - is_first_child:wkly_study_hours 2 495.3 82343 3115.7
## - lunch_type:wkly_study_hours 2 509.0 82357 3115.8
## <none> 81848 3116.2
## - gender:practice_sport 2 570.2 82418 3116.3
## - lunch_type:transport_means 1 328.3 82176 3116.5
## - parent_educ:is_first_child 5 1504.7 83353 3116.9
## - ethnic_group:transport_means 4 1252.8 83101 3117.1
## - ethnic_group:is_first_child 4 1338.1 83186 3117.7
## - parent_marital_status:wkly_study_hours 6 2060.0 83908 3118.8
## + practice_sport:is_first_child 2 182.7 81665 3118.9
## + gender:wkly_study_hours 2 179.7 81668 3118.9
## - parent_marital_status:transport_means 3 1218.2 83066 3118.9
## + practice_sport:wkly_study_hours 4 728.4 81120 3118.9
## + test_prep:practice_sport 2 138.9 81709 3119.2
## + gender:parent_marital_status 3 407.2 81441 3119.2
## + parent_educ:transport_means 5 888.5 80960 3119.7
## - test_prep:wkly_study_hours 2 1175.5 83024 3120.6
## + lunch_type:parent_marital_status 3 191.5 81657 3120.8
## + gender:parent_educ 5 730.7 81117 3120.9
## + ethnic_group:test_prep 4 436.0 81412 3121.0
## + ethnic_group:parent_marital_status 10 2063.5 79785 3121.1
## - is_first_child:transport_means 1 1003.7 82852 3121.4
## + gender:ethnic_group 4 373.8 81474 3121.5
## - lunch_type:practice_sport 2 1498.1 83346 3122.9
## - parent_marital_status:is_first_child 3 1869.2 83717 3123.5
## + parent_educ:test_prep 5 367.9 81480 3123.5
## - parent_educ:parent_marital_status 15 5370.9 87219 3123.7
## + parent_educ:lunch_type 5 307.2 81541 3124.0
## + parent_marital_status:practice_sport 6 474.3 81374 3124.8
## + ethnic_group:practice_sport 8 1015.8 80832 3124.8
## + ethnic_group:wkly_study_hours 8 786.1 81062 3126.5
## + parent_educ:wkly_study_hours 10 1222.9 80625 3127.3
## + ethnic_group:parent_educ 20 2486.4 79362 3138.0
##
## Step: AIC=3113.85
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 207.3 82847 3111.3
## - parent_educ:practice_sport 10 2516.6 85156 3111.6
## - test_prep:transport_means 1 10.1 82650 3111.9
## - gender:transport_means 1 13.8 82653 3111.9
## - gender:is_first_child 1 41.3 82681 3112.2
## - transport_means:wkly_study_hours 2 339.2 82979 3112.3
## - test_prep:parent_marital_status 3 629.1 83269 3112.3
## - lunch_type:is_first_child 1 80.4 82720 3112.4
## - gender:test_prep 1 135.3 82775 3112.8
## - test_prep:is_first_child 1 142.8 82782 3112.9
## - lunch_type:test_prep 1 144.5 82784 3112.9
## - lunch_type:wkly_study_hours 2 428.9 83069 3112.9
## - gender:lunch_type 1 191.2 82831 3113.2
## - gender:practice_sport 2 488.0 83128 3113.3
## - is_first_child:wkly_study_hours 2 498.0 83138 3113.4
## <none> 82640 3113.8
## - ethnic_group:is_first_child 4 1132.4 83772 3113.9
## - ethnic_group:transport_means 4 1167.1 83807 3114.1
## - parent_educ:is_first_child 5 1534.0 84174 3114.7
## - lunch_type:transport_means 1 438.1 83078 3115.0
## - parent_marital_status:transport_means 3 1154.2 83794 3116.0
## + ethnic_group:lunch_type 4 791.6 81848 3116.2
## + practice_sport:is_first_child 2 203.4 82436 3116.4
## + test_prep:practice_sport 2 188.0 82452 3116.5
## + gender:wkly_study_hours 2 178.0 82462 3116.6
## - parent_marital_status:wkly_study_hours 6 2096.2 84736 3116.6
## + parent_educ:transport_means 5 990.3 81649 3116.7
## + gender:parent_marital_status 3 400.6 82239 3117.0
## + practice_sport:wkly_study_hours 4 624.4 82015 3117.4
## + ethnic_group:parent_marital_status 10 2132.2 80507 3118.4
## + lunch_type:parent_marital_status 3 186.2 82454 3118.5
## - test_prep:wkly_study_hours 2 1230.2 83870 3118.6
## - is_first_child:transport_means 1 991.0 83631 3118.9
## + ethnic_group:test_prep 4 387.6 82252 3119.1
## + gender:ethnic_group 4 380.7 82259 3119.1
## + gender:parent_educ 5 625.8 82014 3119.4
## - parent_educ:parent_marital_status 15 5161.0 87801 3119.6
## - parent_marital_status:is_first_child 3 1814.6 84454 3120.7
## + parent_educ:test_prep 5 407.8 82232 3120.9
## - lunch_type:practice_sport 2 1597.2 84237 3121.2
## + parent_educ:lunch_type 5 333.4 82306 3121.5
## + ethnic_group:practice_sport 8 1057.8 81582 3122.2
## + parent_marital_status:practice_sport 6 482.2 82158 3122.4
## + ethnic_group:wkly_study_hours 8 816.7 81823 3124.0
## + parent_educ:wkly_study_hours 10 1061.0 81579 3126.2
## + ethnic_group:parent_educ 20 2629.1 80011 3134.8
##
## Step: AIC=3111.33
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:practice_sport 10 2466.4 85313 3108.6
## - test_prep:transport_means 1 7.1 82854 3109.4
## - gender:transport_means 1 13.8 82861 3109.4
## - gender:is_first_child 1 56.2 82903 3109.7
## - lunch_type:is_first_child 1 71.3 82918 3109.8
## - transport_means:wkly_study_hours 2 357.8 83205 3109.9
## - test_prep:parent_marital_status 3 644.8 83492 3109.9
## - gender:test_prep 1 131.9 82979 3110.3
## - lunch_type:wkly_study_hours 2 420.4 83267 3110.3
## - test_prep:is_first_child 1 147.4 82994 3110.4
## - lunch_type:test_prep 1 170.0 83017 3110.5
## - gender:practice_sport 2 458.5 83305 3110.6
## - gender:lunch_type 1 191.5 83039 3110.7
## - is_first_child:wkly_study_hours 2 491.5 83338 3110.8
## - ethnic_group:is_first_child 4 1114.2 83961 3111.2
## <none> 82847 3111.3
## - ethnic_group:transport_means 4 1218.0 84065 3111.9
## - parent_educ:is_first_child 5 1544.3 84391 3112.2
## - lunch_type:transport_means 1 450.3 83297 3112.5
## - parent_marital_status:transport_means 3 1149.8 83997 3113.5
## + practice_sport:transport_means 2 207.3 82640 3113.8
## + ethnic_group:lunch_type 4 753.5 82094 3113.9
## + gender:wkly_study_hours 2 193.1 82654 3113.9
## + practice_sport:is_first_child 2 183.8 82663 3114.0
## + test_prep:practice_sport 2 173.2 82674 3114.1
## - parent_marital_status:wkly_study_hours 6 2116.7 84964 3114.2
## + gender:parent_marital_status 3 364.2 82483 3114.7
## + practice_sport:wkly_study_hours 4 605.0 82242 3115.0
## + parent_educ:transport_means 5 874.3 81973 3115.1
## + lunch_type:parent_marital_status 3 180.4 82667 3116.0
## - test_prep:wkly_study_hours 2 1235.2 84082 3116.1
## + ethnic_group:test_prep 4 396.0 82451 3116.5
## + gender:ethnic_group 4 377.0 82470 3116.6
## - parent_educ:parent_marital_status 15 5138.6 87986 3116.8
## - is_first_child:transport_means 1 1062.2 83909 3116.8
## + gender:parent_educ 5 597.8 82249 3117.1
## + ethnic_group:parent_marital_status 10 1954.3 80893 3117.2
## - parent_marital_status:is_first_child 3 1809.3 84656 3118.1
## + parent_educ:test_prep 5 434.0 82413 3118.2
## - lunch_type:practice_sport 2 1585.6 84433 3118.5
## + parent_educ:lunch_type 5 376.4 82471 3118.6
## + ethnic_group:practice_sport 8 1073.6 81773 3119.6
## + parent_marital_status:practice_sport 6 447.4 82400 3120.1
## + ethnic_group:wkly_study_hours 8 821.6 82025 3121.4
## + parent_educ:wkly_study_hours 10 1023.1 81824 3124.0
## + ethnic_group:parent_educ 20 2651.9 80195 3132.1
##
## Step: AIC=3108.64
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:parent_marital_status 3 528.2 85842 3106.3
## - transport_means:wkly_study_hours 2 252.8 85566 3106.4
## - test_prep:transport_means 1 6.1 85320 3106.7
## - gender:transport_means 1 53.5 85367 3107.0
## - gender:is_first_child 1 69.0 85382 3107.1
## - gender:practice_sport 2 371.9 85685 3107.2
## - lunch_type:is_first_child 1 89.0 85402 3107.2
## - gender:lunch_type 1 128.6 85442 3107.5
## - lunch_type:test_prep 1 168.7 85482 3107.8
## - gender:test_prep 1 169.6 85483 3107.8
## - test_prep:is_first_child 1 189.4 85503 3107.9
## - is_first_child:wkly_study_hours 2 501.2 85815 3108.1
## - lunch_type:wkly_study_hours 2 501.8 85815 3108.1
## <none> 85313 3108.6
## - ethnic_group:is_first_child 4 1176.4 86490 3108.7
## - lunch_type:transport_means 1 350.4 85664 3109.1
## - ethnic_group:transport_means 4 1384.3 86698 3110.1
## - test_prep:wkly_study_hours 2 930.9 86244 3111.0
## + parent_educ:practice_sport 10 2466.4 82847 3111.3
## + gender:wkly_study_hours 2 187.2 85126 3111.3
## - parent_educ:is_first_child 5 1861.6 87175 3111.4
## + practice_sport:is_first_child 2 173.2 85140 3111.4
## + test_prep:practice_sport 2 172.7 85141 3111.4
## + practice_sport:transport_means 2 157.1 85156 3111.6
## + ethnic_group:lunch_type 4 725.6 84588 3111.6
## - parent_marital_status:wkly_study_hours 6 2229.8 87543 3111.9
## - parent_marital_status:transport_means 3 1345.0 86658 3111.9
## + gender:parent_marital_status 3 380.5 84933 3112.0
## - is_first_child:transport_means 1 813.3 86127 3112.2
## + practice_sport:wkly_study_hours 4 575.3 84738 3112.7
## + parent_educ:transport_means 5 848.1 84465 3112.7
## - lunch_type:practice_sport 2 1258.9 86572 3113.3
## + lunch_type:parent_marital_status 3 167.1 85146 3113.5
## + ethnic_group:test_prep 4 430.7 84883 3113.7
## + gender:ethnic_group 4 394.4 84919 3113.9
## + gender:parent_educ 5 656.9 84657 3114.1
## - parent_marital_status:is_first_child 3 1770.1 87084 3114.8
## + parent_educ:lunch_type 5 556.2 84757 3114.8
## + parent_educ:test_prep 5 401.2 84912 3115.9
## + ethnic_group:practice_sport 8 1164.5 84149 3116.5
## - parent_educ:parent_marital_status 15 5674.3 90988 3116.6
## + ethnic_group:parent_marital_status 10 1651.0 83662 3117.1
## + parent_marital_status:practice_sport 6 334.6 84979 3118.3
## + ethnic_group:wkly_study_hours 8 773.4 84540 3119.3
## + parent_educ:wkly_study_hours 10 1137.2 84176 3120.7
## + ethnic_group:parent_educ 20 2585.1 82728 3130.5
##
## Step: AIC=3106.28
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 246.8 86088 3104.0
## - test_prep:transport_means 1 16.2 85858 3104.4
## - gender:transport_means 1 41.8 85883 3104.6
## - lunch_type:is_first_child 1 80.3 85922 3104.8
## - gender:is_first_child 1 80.8 85922 3104.8
## - gender:practice_sport 2 391.2 86233 3105.0
## - gender:lunch_type 1 133.0 85975 3105.2
## - gender:test_prep 1 156.6 85998 3105.4
## - lunch_type:test_prep 1 167.4 86009 3105.4
## - lunch_type:wkly_study_hours 2 517.9 86359 3105.8
## - is_first_child:wkly_study_hours 2 539.2 86381 3106.0
## - test_prep:is_first_child 1 264.1 86106 3106.1
## <none> 85842 3106.3
## - ethnic_group:is_first_child 4 1209.8 87051 3106.5
## - lunch_type:transport_means 1 355.0 86197 3106.7
## - ethnic_group:transport_means 4 1370.0 87212 3107.6
## - parent_educ:is_first_child 5 1803.5 87645 3108.6
## - test_prep:wkly_study_hours 2 922.7 86764 3108.6
## + test_prep:parent_marital_status 3 528.2 85313 3108.6
## + test_prep:practice_sport 2 227.2 85614 3108.7
## + ethnic_group:lunch_type 4 794.7 85047 3108.8
## + gender:wkly_study_hours 2 191.1 85650 3109.0
## + practice_sport:transport_means 2 166.2 85675 3109.1
## + practice_sport:is_first_child 2 165.9 85676 3109.1
## - parent_marital_status:wkly_study_hours 6 2221.9 88063 3109.4
## - is_first_child:transport_means 1 764.1 86606 3109.5
## + parent_educ:practice_sport 10 2349.8 83492 3109.9
## - parent_marital_status:transport_means 3 1470.4 87312 3110.3
## + gender:parent_marital_status 3 286.9 85555 3110.3
## + parent_educ:transport_means 5 862.9 84979 3110.3
## + practice_sport:wkly_study_hours 4 547.4 85294 3110.5
## - lunch_type:practice_sport 2 1236.0 87078 3110.7
## + lunch_type:parent_marital_status 3 214.5 85627 3110.8
## + gender:ethnic_group 4 426.1 85415 3111.3
## + ethnic_group:test_prep 4 419.6 85422 3111.4
## + gender:parent_educ 5 621.8 85220 3112.0
## + parent_educ:lunch_type 5 563.6 85278 3112.4
## - parent_educ:parent_marital_status 15 5469.5 91311 3112.7
## - parent_marital_status:is_first_child 3 1845.3 87687 3112.8
## + parent_educ:test_prep 5 377.3 85464 3113.7
## + ethnic_group:practice_sport 8 1128.8 84713 3114.5
## + parent_marital_status:practice_sport 6 382.9 85459 3115.6
## + ethnic_group:parent_marital_status 11 1760.9 84081 3116.1
## + ethnic_group:wkly_study_hours 8 867.5 84974 3116.3
## + parent_educ:wkly_study_hours 10 1216.0 84626 3117.9
## + ethnic_group:parent_educ 20 2671.7 83170 3127.6
##
## Step: AIC=3103.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:transport_means 1 7.5 86096 3102.0
## - gender:transport_means 1 39.1 86127 3102.2
## - gender:is_first_child 1 67.5 86156 3102.4
## - lunch_type:is_first_child 1 74.0 86162 3102.5
## - gender:lunch_type 1 121.2 86210 3102.8
## - gender:practice_sport 2 425.9 86514 3102.9
## - gender:test_prep 1 140.2 86228 3102.9
## - lunch_type:test_prep 1 153.5 86242 3103.0
## - lunch_type:wkly_study_hours 2 549.2 86638 3103.7
## - test_prep:is_first_child 1 279.5 86368 3103.9
## <none> 86088 3104.0
## - is_first_child:wkly_study_hours 2 592.9 86681 3104.0
## - lunch_type:transport_means 1 345.6 86434 3104.3
## - ethnic_group:is_first_child 4 1229.5 87318 3104.3
## - test_prep:wkly_study_hours 2 872.0 86960 3105.9
## - ethnic_group:transport_means 4 1465.2 87554 3105.9
## + test_prep:practice_sport 2 258.1 85830 3106.2
## + ethnic_group:lunch_type 4 835.7 85253 3106.2
## + transport_means:wkly_study_hours 2 246.8 85842 3106.3
## + test_prep:parent_marital_status 3 522.1 85566 3106.4
## - parent_educ:is_first_child 5 1848.6 87937 3106.5
## + practice_sport:transport_means 2 184.0 85904 3106.7
## + practice_sport:is_first_child 2 182.1 85906 3106.7
## + gender:wkly_study_hours 2 180.1 85908 3106.7
## - is_first_child:transport_means 1 769.9 86858 3107.2
## - parent_marital_status:wkly_study_hours 6 2303.2 88392 3107.6
## - parent_marital_status:transport_means 3 1454.0 87542 3107.9
## + practice_sport:wkly_study_hours 4 564.7 85524 3108.1
## + gender:parent_marital_status 3 272.1 85816 3108.1
## + parent_educ:practice_sport 10 2249.6 83839 3108.3
## + parent_educ:transport_means 5 808.8 85280 3108.4
## + lunch_type:parent_marital_status 3 219.1 85869 3108.5
## - lunch_type:practice_sport 2 1254.1 87342 3108.5
## + gender:ethnic_group 4 458.6 85630 3108.8
## + ethnic_group:test_prep 4 414.0 85674 3109.1
## + gender:parent_educ 5 674.2 85414 3109.3
## + parent_educ:lunch_type 5 590.9 85497 3109.9
## - parent_marital_status:is_first_child 3 1791.3 87880 3110.1
## - parent_educ:parent_marital_status 15 5445.9 91534 3110.2
## + parent_educ:test_prep 5 377.4 85711 3111.4
## + ethnic_group:practice_sport 8 1152.6 84936 3112.0
## + parent_marital_status:practice_sport 6 396.9 85691 3113.2
## + ethnic_group:parent_marital_status 11 1695.5 84393 3114.2
## + ethnic_group:wkly_study_hours 8 714.6 85374 3115.1
## + parent_educ:wkly_study_hours 10 1220.0 84868 3115.6
## + ethnic_group:parent_educ 20 2613.0 83475 3125.8
##
## Step: AIC=3102.03
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 42.1 86138 3100.3
## - gender:is_first_child 1 67.9 86164 3100.5
## - lunch_type:is_first_child 1 77.5 86173 3100.6
## - gender:lunch_type 1 124.5 86220 3100.9
## - gender:practice_sport 2 423.6 86519 3100.9
## - gender:test_prep 1 138.2 86234 3101.0
## - lunch_type:test_prep 1 154.4 86250 3101.1
## - lunch_type:wkly_study_hours 2 541.9 86638 3101.7
## - test_prep:is_first_child 1 280.9 86377 3101.9
## <none> 86096 3102.0
## - is_first_child:wkly_study_hours 2 601.9 86698 3102.1
## - ethnic_group:is_first_child 4 1222.9 87319 3102.3
## - lunch_type:transport_means 1 341.8 86438 3102.4
## - test_prep:wkly_study_hours 2 866.7 86963 3103.9
## + test_prep:transport_means 1 7.5 86088 3104.0
## - ethnic_group:transport_means 4 1483.7 87580 3104.1
## + test_prep:practice_sport 2 258.8 85837 3104.2
## + ethnic_group:lunch_type 4 837.4 85258 3104.3
## + transport_means:wkly_study_hours 2 238.0 85858 3104.4
## + test_prep:parent_marital_status 3 528.2 85568 3104.4
## - parent_educ:is_first_child 5 1853.3 87949 3104.6
## + practice_sport:is_first_child 2 182.2 85914 3104.8
## + gender:wkly_study_hours 2 181.4 85914 3104.8
## + practice_sport:transport_means 2 180.8 85915 3104.8
## - is_first_child:transport_means 1 780.2 86876 3105.3
## - parent_marital_status:wkly_study_hours 6 2299.8 88396 3105.6
## - parent_marital_status:transport_means 3 1462.4 87558 3106.0
## + practice_sport:wkly_study_hours 4 564.1 85532 3106.2
## + gender:parent_marital_status 3 270.0 85826 3106.2
## + parent_educ:practice_sport 10 2248.9 83847 3106.4
## + parent_educ:transport_means 5 812.6 85283 3106.4
## + lunch_type:parent_marital_status 3 221.2 85875 3106.5
## - lunch_type:practice_sport 2 1259.1 87355 3106.6
## + gender:ethnic_group 4 457.3 85638 3106.9
## + ethnic_group:test_prep 4 413.8 85682 3107.2
## + gender:parent_educ 5 671.4 85424 3107.4
## + parent_educ:lunch_type 5 584.8 85511 3108.0
## - parent_marital_status:is_first_child 3 1800.2 87896 3108.2
## - parent_educ:parent_marital_status 15 5477.3 91573 3108.4
## + parent_educ:test_prep 5 381.9 85714 3109.4
## + ethnic_group:practice_sport 8 1155.8 84940 3110.1
## + parent_marital_status:practice_sport 6 398.4 85697 3111.3
## + ethnic_group:parent_marital_status 11 1694.7 84401 3112.3
## + ethnic_group:wkly_study_hours 8 716.5 85379 3113.1
## + parent_educ:wkly_study_hours 10 1221.4 84874 3113.6
## + ethnic_group:parent_educ 20 2587.1 83509 3124.0
##
## Step: AIC=3100.31
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 67.1 86205 3098.8
## - lunch_type:is_first_child 1 87.1 86225 3098.9
## - gender:test_prep 1 125.8 86264 3099.2
## - gender:lunch_type 1 127.9 86266 3099.2
## - gender:practice_sport 2 441.0 86579 3099.3
## - lunch_type:test_prep 1 157.7 86296 3099.4
## - lunch_type:wkly_study_hours 2 527.4 86665 3099.9
## - test_prep:is_first_child 1 287.0 86425 3100.3
## <none> 86138 3100.3
## - is_first_child:wkly_study_hours 2 614.1 86752 3100.5
## - ethnic_group:is_first_child 4 1217.0 87355 3100.6
## - lunch_type:transport_means 1 350.7 86489 3100.7
## + gender:transport_means 1 42.1 86096 3102.0
## - test_prep:wkly_study_hours 2 865.7 87004 3102.2
## + test_prep:transport_means 1 10.5 86127 3102.2
## - ethnic_group:transport_means 4 1467.2 87605 3102.3
## + test_prep:practice_sport 2 254.5 85883 3102.6
## + ethnic_group:lunch_type 4 830.4 85308 3102.6
## + transport_means:wkly_study_hours 2 233.9 85904 3102.7
## + test_prep:parent_marital_status 3 517.8 85620 3102.8
## - parent_educ:is_first_child 5 1840.1 87978 3102.8
## + gender:wkly_study_hours 2 185.9 85952 3103.0
## + practice_sport:is_first_child 2 184.7 85953 3103.1
## + practice_sport:transport_means 2 182.4 85956 3103.1
## - is_first_child:transport_means 1 803.3 86941 3103.8
## - parent_marital_status:wkly_study_hours 6 2297.0 88435 3103.8
## - parent_marital_status:transport_means 3 1462.1 87600 3104.2
## + parent_educ:practice_sport 10 2282.9 83855 3104.5
## + gender:parent_marital_status 3 264.9 85873 3104.5
## + practice_sport:wkly_study_hours 4 542.5 85595 3104.6
## + parent_educ:transport_means 5 823.1 85315 3104.7
## - lunch_type:practice_sport 2 1240.0 87378 3104.8
## + lunch_type:parent_marital_status 3 222.7 85915 3104.8
## + gender:ethnic_group 4 473.5 85664 3105.1
## + ethnic_group:test_prep 4 412.7 85725 3105.5
## + gender:parent_educ 5 671.3 85467 3105.7
## + parent_educ:lunch_type 5 591.3 85547 3106.2
## - parent_educ:parent_marital_status 15 5443.9 91582 3106.5
## - parent_marital_status:is_first_child 3 1820.2 87958 3106.7
## + parent_educ:test_prep 5 385.7 85752 3107.7
## + ethnic_group:practice_sport 8 1140.5 84997 3108.4
## + parent_marital_status:practice_sport 6 390.6 85747 3109.6
## + ethnic_group:parent_marital_status 11 1717.1 84421 3110.4
## + ethnic_group:wkly_study_hours 8 709.6 85428 3111.4
## + parent_educ:wkly_study_hours 10 1196.9 84941 3112.1
## + ethnic_group:parent_educ 20 2560.8 83577 3122.5
##
## Step: AIC=3098.77
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:is_first_child 1 97.8 86303 3097.4
## - gender:test_prep 1 115.8 86321 3097.6
## - gender:lunch_type 1 127.1 86332 3097.6
## - gender:practice_sport 2 456.8 86662 3097.9
## - lunch_type:test_prep 1 169.6 86375 3097.9
## - lunch_type:wkly_study_hours 2 528.1 86733 3098.4
## <none> 86205 3098.8
## - ethnic_group:is_first_child 4 1184.1 87389 3098.8
## - test_prep:is_first_child 1 315.6 86521 3098.9
## - is_first_child:wkly_study_hours 2 648.1 86853 3099.2
## - lunch_type:transport_means 1 367.7 86573 3099.3
## + gender:is_first_child 1 67.1 86138 3100.3
## + gender:transport_means 1 41.3 86164 3100.5
## - test_prep:wkly_study_hours 2 849.9 87055 3100.6
## + test_prep:transport_means 1 10.9 86194 3100.7
## - ethnic_group:transport_means 4 1518.3 87723 3101.1
## + test_prep:practice_sport 2 241.4 85964 3101.1
## + ethnic_group:lunch_type 4 819.4 85386 3101.1
## + test_prep:parent_marital_status 3 527.3 85678 3101.2
## + transport_means:wkly_study_hours 2 221.2 85984 3101.3
## + practice_sport:transport_means 2 193.8 86011 3101.4
## + practice_sport:is_first_child 2 192.0 86013 3101.5
## + gender:wkly_study_hours 2 185.4 86020 3101.5
## - parent_educ:is_first_child 5 1889.5 88095 3101.6
## - parent_marital_status:wkly_study_hours 6 2259.4 88464 3102.0
## - is_first_child:transport_means 1 777.0 86982 3102.1
## + gender:parent_marital_status 3 287.2 85918 3102.8
## + parent_educ:practice_sport 10 2295.0 83910 3102.8
## + practice_sport:wkly_study_hours 4 562.1 85643 3102.9
## - parent_marital_status:transport_means 3 1506.1 87711 3103.0
## + parent_educ:transport_means 5 813.9 85391 3103.2
## + lunch_type:parent_marital_status 3 232.4 85973 3103.2
## + gender:ethnic_group 4 489.0 85716 3103.4
## - lunch_type:practice_sport 2 1289.5 87495 3103.5
## + ethnic_group:test_prep 4 394.8 85810 3104.1
## + gender:parent_educ 5 664.8 85540 3104.2
## + parent_educ:lunch_type 5 631.3 85574 3104.4
## - parent_educ:parent_marital_status 15 5457.7 91663 3105.0
## - parent_marital_status:is_first_child 3 1805.4 88011 3105.0
## + parent_educ:test_prep 5 387.6 85818 3106.1
## + ethnic_group:practice_sport 8 1096.1 85109 3107.2
## + parent_marital_status:practice_sport 6 389.2 85816 3108.1
## + ethnic_group:parent_marital_status 11 1738.0 84467 3108.8
## + ethnic_group:wkly_study_hours 8 685.9 85519 3110.1
## + parent_educ:wkly_study_hours 10 1203.7 85001 3110.5
## + ethnic_group:parent_educ 20 2490.6 83714 3121.5
##
## Step: AIC=3097.44
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 120.4 86423 3096.3
## - gender:test_prep 1 122.5 86425 3096.3
## - gender:practice_sport 2 425.3 86728 3096.3
## - lunch_type:test_prep 1 164.4 86467 3096.6
## - lunch_type:wkly_study_hours 2 507.0 86810 3096.9
## - ethnic_group:is_first_child 4 1131.4 87434 3097.1
## <none> 86303 3097.4
## - test_prep:is_first_child 1 293.8 86597 3097.4
## - is_first_child:wkly_study_hours 2 610.4 86913 3097.6
## - lunch_type:transport_means 1 380.8 86684 3098.0
## + lunch_type:is_first_child 1 97.8 86205 3098.8
## + gender:is_first_child 1 77.8 86225 3098.9
## + gender:transport_means 1 51.4 86251 3099.1
## - test_prep:wkly_study_hours 2 862.1 87165 3099.3
## + test_prep:transport_means 1 16.2 86287 3099.3
## + ethnic_group:lunch_type 4 823.2 85480 3099.8
## + test_prep:practice_sport 2 235.1 86068 3099.8
## + test_prep:parent_marital_status 3 520.4 85782 3099.9
## - ethnic_group:transport_means 4 1548.9 87852 3099.9
## + transport_means:wkly_study_hours 2 211.8 86091 3100.0
## + gender:wkly_study_hours 2 188.5 86114 3100.2
## + practice_sport:transport_means 2 184.2 86119 3100.2
## - parent_educ:is_first_child 5 1885.0 88188 3100.2
## + practice_sport:is_first_child 2 175.0 86128 3100.2
## - parent_marital_status:wkly_study_hours 6 2200.8 88504 3100.3
## - is_first_child:transport_means 1 770.4 87073 3100.7
## + practice_sport:wkly_study_hours 4 603.6 85699 3101.3
## + parent_educ:practice_sport 10 2322.3 83981 3101.3
## + gender:parent_marital_status 3 297.0 86006 3101.4
## - parent_marital_status:transport_means 3 1515.9 87819 3101.7
## + parent_educ:transport_means 5 822.3 85481 3101.8
## + lunch_type:parent_marital_status 3 227.7 86075 3101.9
## - lunch_type:practice_sport 2 1285.2 87588 3102.2
## + gender:ethnic_group 4 468.8 85834 3102.2
## + ethnic_group:test_prep 4 412.9 85890 3102.6
## + gender:parent_educ 5 671.5 85631 3102.8
## + parent_educ:lunch_type 5 648.6 85654 3103.0
## - parent_marital_status:is_first_child 3 1733.5 88036 3103.2
## - parent_educ:parent_marital_status 15 5422.1 91725 3103.4
## + parent_educ:test_prep 5 411.8 85891 3104.6
## + ethnic_group:practice_sport 8 1075.2 85228 3106.1
## + parent_marital_status:practice_sport 6 390.2 85913 3106.8
## + ethnic_group:parent_marital_status 11 1745.0 84558 3107.4
## + ethnic_group:wkly_study_hours 8 686.4 85616 3108.7
## + parent_educ:wkly_study_hours 10 1226.0 85077 3109.0
## + ethnic_group:parent_educ 20 2445.0 83858 3120.5
##
## Step: AIC=3096.27
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 108.1 86531 3095.0
## - gender:practice_sport 2 419.0 86842 3095.1
## - lunch_type:test_prep 1 190.0 86613 3095.6
## - lunch_type:wkly_study_hours 2 492.0 86915 3095.6
## - ethnic_group:is_first_child 4 1110.9 87534 3095.8
## <none> 86423 3096.3
## - test_prep:is_first_child 1 303.9 86727 3096.3
## - is_first_child:wkly_study_hours 2 606.7 87030 3096.4
## - lunch_type:transport_means 1 408.7 86832 3097.1
## + gender:lunch_type 1 120.4 86303 3097.4
## + lunch_type:is_first_child 1 91.2 86332 3097.6
## + gender:is_first_child 1 76.5 86347 3097.7
## + gender:transport_means 1 54.6 86369 3097.9
## + test_prep:transport_means 1 20.8 86403 3098.1
## - test_prep:wkly_study_hours 2 879.1 87302 3098.2
## + test_prep:practice_sport 2 250.2 86173 3098.6
## + ethnic_group:lunch_type 4 828.1 85595 3098.6
## + test_prep:parent_marital_status 3 526.2 85897 3098.7
## + transport_means:wkly_study_hours 2 200.0 86223 3098.9
## - ethnic_group:transport_means 4 1576.0 87999 3098.9
## + practice_sport:transport_means 2 181.2 86242 3099.0
## + gender:wkly_study_hours 2 166.1 86257 3099.1
## + practice_sport:is_first_child 2 161.1 86262 3099.2
## - parent_educ:is_first_child 5 1917.3 88341 3099.2
## - is_first_child:transport_means 1 743.5 87167 3099.3
## - parent_marital_status:wkly_study_hours 6 2284.1 88707 3099.7
## + practice_sport:wkly_study_hours 4 602.7 85821 3100.1
## - parent_marital_status:transport_means 3 1475.8 87899 3100.3
## + gender:parent_marital_status 3 286.4 86137 3100.3
## + parent_educ:transport_means 5 855.6 85568 3100.4
## + parent_educ:practice_sport 10 2280.1 84143 3100.5
## + lunch_type:parent_marital_status 3 258.2 86165 3100.5
## + gender:ethnic_group 4 457.4 85966 3101.1
## + ethnic_group:test_prep 4 418.7 86005 3101.4
## + parent_educ:lunch_type 5 696.7 85727 3101.5
## - lunch_type:practice_sport 2 1371.9 87795 3101.6
## - parent_marital_status:is_first_child 3 1685.0 88108 3101.7
## + gender:parent_educ 5 664.3 85759 3101.7
## - parent_educ:parent_marital_status 15 5394.8 91818 3102.0
## + parent_educ:test_prep 5 394.9 86028 3103.6
## + ethnic_group:practice_sport 8 1026.1 85397 3105.2
## + parent_marital_status:practice_sport 6 401.4 86022 3105.5
## + ethnic_group:parent_marital_status 11 1748.2 84675 3106.2
## + ethnic_group:wkly_study_hours 8 702.1 85721 3107.4
## + parent_educ:wkly_study_hours 10 1177.1 85246 3108.2
## + ethnic_group:parent_educ 20 2371.1 84052 3119.8
##
## Step: AIC=3095
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:practice_sport 2 441.2 86973 3094.0
## - ethnic_group:is_first_child 4 1074.7 87606 3094.3
## - lunch_type:test_prep 1 207.3 86739 3094.4
## - lunch_type:wkly_study_hours 2 504.2 87036 3094.4
## <none> 86531 3095.0
## - test_prep:is_first_child 1 303.6 86835 3095.1
## - is_first_child:wkly_study_hours 2 612.5 87144 3095.2
## - lunch_type:transport_means 1 426.8 86958 3095.9
## + gender:test_prep 1 108.1 86423 3096.3
## + gender:lunch_type 1 106.0 86425 3096.3
## + lunch_type:is_first_child 1 97.7 86434 3096.3
## + gender:is_first_child 1 66.6 86465 3096.6
## + gender:transport_means 1 41.4 86490 3096.7
## - test_prep:wkly_study_hours 2 845.9 87377 3096.7
## + test_prep:transport_means 1 17.0 86514 3096.9
## + ethnic_group:lunch_type 4 846.4 85685 3097.2
## + test_prep:practice_sport 2 243.1 86288 3097.3
## + test_prep:parent_marital_status 3 516.8 86015 3097.5
## - parent_educ:is_first_child 5 1876.5 88408 3097.7
## + gender:wkly_study_hours 2 188.8 86343 3097.7
## + transport_means:wkly_study_hours 2 188.1 86343 3097.7
## - ethnic_group:transport_means 4 1587.4 88119 3097.7
## + practice_sport:transport_means 2 173.6 86358 3097.8
## + practice_sport:is_first_child 2 167.8 86364 3097.9
## - is_first_child:transport_means 1 725.6 87257 3097.9
## - parent_marital_status:wkly_study_hours 6 2257.5 88789 3098.2
## + practice_sport:wkly_study_hours 4 589.5 85942 3099.0
## + gender:parent_marital_status 3 295.0 86236 3099.0
## + parent_educ:practice_sport 10 2314.6 84217 3099.0
## - parent_marital_status:transport_means 3 1496.6 88028 3099.1
## + lunch_type:parent_marital_status 3 270.6 86261 3099.2
## + parent_educ:transport_means 5 842.4 85689 3099.2
## + gender:ethnic_group 4 451.2 86080 3099.9
## - parent_marital_status:is_first_child 3 1638.4 88170 3100.1
## - lunch_type:practice_sport 2 1356.7 87888 3100.2
## + parent_educ:lunch_type 5 696.7 85835 3100.2
## + ethnic_group:test_prep 4 384.9 86146 3100.4
## - parent_educ:parent_marital_status 15 5349.4 91881 3100.4
## + gender:parent_educ 5 657.1 85874 3100.5
## + parent_educ:test_prep 5 396.0 86135 3102.3
## + parent_marital_status:practice_sport 6 425.7 86106 3104.1
## + ethnic_group:practice_sport 8 993.6 85538 3104.2
## + ethnic_group:parent_marital_status 11 1802.0 84729 3104.6
## + ethnic_group:wkly_study_hours 8 733.7 85798 3106.0
## + parent_educ:wkly_study_hours 10 1223.2 85308 3106.6
## + ethnic_group:parent_educ 20 2369.4 84162 3118.6
##
## Step: AIC=3094
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:is_first_child 4 1045.7 88018 3093.1
## - lunch_type:wkly_study_hours 2 485.3 87458 3093.3
## - lunch_type:test_prep 1 212.0 87185 3093.4
## - test_prep:is_first_child 1 279.8 87252 3093.9
## <none> 86973 3094.0
## - is_first_child:wkly_study_hours 2 618.8 87591 3094.2
## + gender:practice_sport 2 441.2 86531 3095.0
## + gender:test_prep 1 130.3 86842 3095.1
## - lunch_type:transport_means 1 467.1 87440 3095.2
## + gender:lunch_type 1 98.8 86874 3095.3
## + gender:is_first_child 1 77.3 86895 3095.5
## + lunch_type:is_first_child 1 67.1 86905 3095.6
## + gender:transport_means 1 55.4 86917 3095.6
## - test_prep:wkly_study_hours 2 847.3 87820 3095.7
## + test_prep:transport_means 1 12.9 86960 3095.9
## + test_prep:practice_sport 2 266.7 86706 3096.2
## - parent_marital_status:wkly_study_hours 6 2123.6 89096 3096.2
## + test_prep:parent_marital_status 3 531.6 86441 3096.4
## + gender:wkly_study_hours 2 221.6 86751 3096.5
## + transport_means:wkly_study_hours 2 219.6 86753 3096.5
## - ethnic_group:transport_means 4 1578.3 88551 3096.6
## - parent_educ:is_first_child 5 1897.3 88870 3096.7
## + ethnic_group:lunch_type 4 771.2 86201 3096.8
## + practice_sport:is_first_child 2 167.3 86805 3096.9
## + practice_sport:transport_means 2 155.6 86817 3096.9
## - is_first_child:transport_means 1 764.2 87737 3097.2
## - parent_marital_status:transport_means 3 1428.3 88401 3097.6
## + gender:parent_marital_status 3 346.2 86626 3097.7
## + practice_sport:wkly_study_hours 4 637.1 86335 3097.7
## + parent_educ:transport_means 5 864.0 86109 3098.1
## + lunch_type:parent_marital_status 3 267.4 86705 3098.2
## + parent_educ:practice_sport 10 2207.6 84765 3098.8
## + parent_educ:lunch_type 5 741.3 86231 3098.9
## + gender:ethnic_group 4 414.5 86558 3099.2
## - parent_educ:parent_marital_status 15 5364.1 92337 3099.3
## - parent_marital_status:is_first_child 3 1684.3 88657 3099.3
## + ethnic_group:test_prep 4 382.9 86590 3099.4
## + gender:parent_educ 5 657.1 86316 3099.5
## - lunch_type:practice_sport 2 1466.3 88439 3099.9
## + parent_educ:test_prep 5 353.3 86619 3101.6
## + ethnic_group:practice_sport 8 1131.7 85841 3102.3
## + parent_marital_status:practice_sport 6 408.6 86564 3103.2
## + ethnic_group:parent_marital_status 11 1849.7 85123 3103.3
## + ethnic_group:wkly_study_hours 8 736.7 86236 3105.0
## + parent_educ:wkly_study_hours 10 1160.6 85812 3106.1
## - gender 1 2914.0 89887 3111.4
## + ethnic_group:parent_educ 20 2455.9 84517 3117.1
##
## Step: AIC=3093.05
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:wkly_study_hours 2 439.6 88458 3092.0
## - lunch_type:test_prep 1 220.6 88239 3092.5
## <none> 88018 3093.1
## - test_prep:is_first_child 1 327.4 88346 3093.2
## - test_prep:wkly_study_hours 2 638.7 88657 3093.3
## - lunch_type:transport_means 1 406.7 88425 3093.8
## + ethnic_group:is_first_child 4 1045.7 86973 3094.0
## - is_first_child:wkly_study_hours 2 753.2 88772 3094.1
## + gender:practice_sport 2 412.2 87606 3094.3
## - is_first_child:transport_means 1 504.9 88523 3094.4
## + gender:test_prep 1 91.6 87927 3094.4
## + gender:lunch_type 1 84.2 87934 3094.5
## + gender:transport_means 1 45.0 87973 3094.8
## + gender:is_first_child 1 42.5 87976 3094.8
## - parent_marital_status:wkly_study_hours 6 2077.1 90095 3094.8
## + lunch_type:is_first_child 1 25.4 87993 3094.9
## + test_prep:transport_means 1 2.9 88015 3095.0
## + test_prep:practice_sport 2 279.7 87739 3095.2
## + test_prep:parent_marital_status 3 571.5 87447 3095.2
## + transport_means:wkly_study_hours 2 250.1 87768 3095.4
## + practice_sport:is_first_child 2 227.8 87790 3095.5
## - ethnic_group:transport_means 4 1651.1 89669 3096.0
## + gender:wkly_study_hours 2 139.5 87879 3096.1
## + practice_sport:transport_means 2 136.1 87882 3096.1
## + practice_sport:wkly_study_hours 4 699.2 87319 3096.3
## - parent_educ:is_first_child 5 2019.8 90038 3096.4
## - parent_marital_status:transport_means 3 1460.3 89479 3096.8
## + parent_educ:transport_means 5 915.0 87103 3096.9
## + gender:parent_marital_status 3 278.5 87740 3097.2
## + ethnic_group:lunch_type 4 559.4 87459 3097.3
## - parent_educ:parent_marital_status 15 5295.5 93314 3097.5
## + lunch_type:parent_marital_status 3 226.5 87792 3097.5
## + parent_educ:lunch_type 5 815.5 87203 3097.6
## + parent_educ:practice_sport 10 2279.3 85739 3097.6
## + ethnic_group:test_prep 4 411.9 87606 3098.3
## - lunch_type:practice_sport 2 1396.6 89415 3098.3
## + gender:ethnic_group 4 377.8 87641 3098.5
## - parent_marital_status:is_first_child 3 1836.6 89855 3099.2
## + gender:parent_educ 5 561.0 87457 3099.3
## + parent_educ:test_prep 5 377.5 87641 3100.5
## + ethnic_group:practice_sport 8 1053.2 86965 3101.9
## + parent_marital_status:practice_sport 6 283.5 87735 3103.2
## + ethnic_group:wkly_study_hours 8 783.8 87235 3103.8
## + ethnic_group:parent_marital_status 11 1528.1 86490 3104.7
## + parent_educ:wkly_study_hours 10 1203.3 86815 3104.9
## - gender 1 3194.3 91213 3112.1
## + ethnic_group:parent_educ 20 2547.3 85471 3115.7
##
## Step: AIC=3091.99
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 183.8 88642 3091.2
## <none> 88458 3092.0
## - test_prep:is_first_child 1 353.8 88812 3092.3
## - lunch_type:transport_means 1 389.2 88847 3092.6
## - test_prep:wkly_study_hours 2 693.4 89151 3092.6
## - parent_marital_status:wkly_study_hours 6 1937.5 90395 3092.8
## + lunch_type:wkly_study_hours 2 439.6 88018 3093.1
## - is_first_child:wkly_study_hours 2 763.2 89221 3093.1
## + ethnic_group:is_first_child 4 1000.0 87458 3093.3
## + gender:test_prep 1 103.6 88354 3093.3
## + gender:practice_sport 2 395.2 88063 3093.3
## + gender:lunch_type 1 74.0 88384 3093.5
## - is_first_child:transport_means 1 556.8 89015 3093.7
## + gender:is_first_child 1 40.5 88417 3093.7
## + gender:transport_means 1 29.5 88428 3093.8
## + test_prep:practice_sport 2 322.7 88135 3093.8
## + lunch_type:is_first_child 1 16.5 88441 3093.9
## + test_prep:transport_means 1 1.5 88456 3094.0
## + transport_means:wkly_study_hours 2 289.0 88169 3094.1
## + test_prep:parent_marital_status 3 573.8 87884 3094.2
## + practice_sport:is_first_child 2 234.2 88224 3094.4
## - ethnic_group:transport_means 4 1593.9 90052 3094.5
## - parent_educ:is_first_child 5 1983.0 90441 3095.1
## + practice_sport:transport_means 2 128.9 88329 3095.1
## + gender:wkly_study_hours 2 103.0 88355 3095.3
## + parent_educ:transport_means 5 988.3 87470 3095.4
## - parent_marital_status:transport_means 3 1439.2 89897 3095.5
## + practice_sport:wkly_study_hours 4 664.7 87793 3095.5
## + gender:parent_marital_status 3 332.0 88126 3095.8
## + parent_educ:practice_sport 10 2350.0 86108 3096.1
## + lunch_type:parent_marital_status 3 206.8 88251 3096.6
## + ethnic_group:lunch_type 4 504.4 87953 3096.6
## - parent_educ:parent_marital_status 15 5358.7 93817 3096.7
## + ethnic_group:test_prep 4 423.2 88035 3097.2
## + parent_educ:lunch_type 5 709.1 87749 3097.2
## - lunch_type:practice_sport 2 1411.9 89870 3097.3
## + gender:ethnic_group 4 346.1 88112 3097.7
## + gender:parent_educ 5 616.5 87841 3097.9
## - parent_marital_status:is_first_child 3 1837.0 90295 3098.1
## + parent_educ:test_prep 5 386.1 88072 3099.4
## + ethnic_group:practice_sport 8 1034.5 87423 3101.1
## + parent_marital_status:practice_sport 6 290.1 88168 3102.1
## + ethnic_group:wkly_study_hours 8 803.7 87654 3102.6
## + ethnic_group:parent_marital_status 11 1478.6 86979 3104.1
## + parent_educ:wkly_study_hours 10 1132.5 87325 3104.4
## - gender 1 3238.9 91697 3111.2
## + ethnic_group:parent_educ 20 2566.2 85892 3114.6
##
## Step: AIC=3091.22
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:practice_sport + lunch_type:transport_means +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## <none> 88642 3091.2
## - test_prep:is_first_child 1 340.8 88982 3091.5
## - lunch_type:transport_means 1 343.0 88985 3091.5
## - test_prep:wkly_study_hours 2 699.0 89341 3091.8
## + lunch_type:test_prep 1 183.8 88458 3092.0
## - parent_marital_status:wkly_study_hours 6 1959.2 90601 3092.1
## + gender:test_prep 1 118.0 88524 3092.4
## + ethnic_group:is_first_child 4 1007.9 87634 3092.5
## + lunch_type:wkly_study_hours 2 402.8 88239 3092.5
## + gender:practice_sport 2 399.7 88242 3092.6
## - is_first_child:wkly_study_hours 2 806.1 89448 3092.6
## - is_first_child:transport_means 1 504.9 89147 3092.6
## + gender:lunch_type 1 94.2 88547 3092.6
## + gender:is_first_child 1 46.8 88595 3092.9
## + gender:transport_means 1 33.6 88608 3093.0
## + test_prep:practice_sport 2 332.6 88309 3093.0
## + lunch_type:is_first_child 1 14.2 88627 3093.1
## + test_prep:transport_means 1 0.9 88641 3093.2
## + test_prep:parent_marital_status 3 572.8 88069 3093.4
## + transport_means:wkly_study_hours 2 262.7 88379 3093.5
## + practice_sport:is_first_child 2 245.6 88396 3093.6
## - ethnic_group:transport_means 4 1620.7 90262 3093.9
## - parent_educ:is_first_child 5 1937.1 90579 3094.0
## + practice_sport:transport_means 2 152.2 88490 3094.2
## + gender:wkly_study_hours 2 104.4 88537 3094.5
## + practice_sport:wkly_study_hours 4 694.6 87947 3094.6
## + parent_educ:transport_means 5 980.6 87661 3094.7
## - parent_marital_status:transport_means 3 1457.2 90099 3094.8
## + gender:parent_marital_status 3 336.0 88306 3095.0
## - parent_educ:parent_marital_status 15 5267.7 93909 3095.3
## + parent_educ:practice_sport 10 2356.5 86285 3095.3
## + ethnic_group:lunch_type 4 527.6 88114 3095.7
## + lunch_type:parent_marital_status 3 190.8 88451 3095.9
## - lunch_type:practice_sport 2 1378.2 90020 3096.3
## + ethnic_group:test_prep 4 405.7 88236 3096.5
## + parent_educ:lunch_type 5 676.9 87965 3096.7
## + gender:ethnic_group 4 349.9 88292 3096.9
## + gender:parent_educ 5 646.5 87995 3096.9
## - parent_marital_status:is_first_child 3 1860.2 90502 3097.5
## + parent_educ:test_prep 5 412.2 88229 3098.5
## + ethnic_group:practice_sport 8 1081.3 87560 3100.0
## + parent_marital_status:practice_sport 6 299.4 88342 3101.2
## + ethnic_group:wkly_study_hours 8 857.1 87785 3101.5
## + parent_educ:wkly_study_hours 10 1206.0 87436 3103.1
## + ethnic_group:parent_marital_status 11 1444.1 87198 3103.5
## - gender 1 3294.9 91937 3110.8
## + ethnic_group:parent_educ 20 2571.4 86070 3113.8
summary(stepwise_model_math)
##
## Call:
## lm(formula = math_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:practice_sport + lunch_type:transport_means +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours,
## data = df_4_mdl_math)
##
## Residuals:
## Min 1Q Median 3Q Max
## -48.225 -8.356 0.435 8.408 29.970
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 43.4922 7.6094
## gendermale 5.0562 1.1468
## ethnic_groupgroup B 3.1099 3.8855
## ethnic_groupgroup C 4.7867 3.5363
## ethnic_groupgroup D 4.4789 3.6141
## ethnic_groupgroup E 19.5605 4.0197
## parent_educbachelor's degree 22.6142 6.3793
## parent_educhigh school -11.9676 5.2257
## parent_educmaster's degree -1.9384 7.3940
## parent_educsome college 0.8824 5.2535
## parent_educsome high school 1.6696 5.2602
## lunch_typestandard 5.7052 3.8861
## test_prepnone -1.1067 3.0821
## parent_marital_statusmarried 9.7202 5.4642
## parent_marital_statussingle 3.7791 6.1207
## parent_marital_statuswidowed 29.2538 21.3074
## practice_sportregularly -4.2709 3.3825
## practice_sportsometimes -6.0415 3.2607
## is_first_childyes 12.5726 5.4684
## transport_meansschool_bus 5.2495 5.3829
## wkly_study_hours> 10 -4.8803 6.2686
## wkly_study_hours10-May 4.6584 4.6603
## ethnic_groupgroup B:transport_meansschool_bus -4.3677 4.8098
## ethnic_groupgroup C:transport_meansschool_bus -7.7457 4.4977
## ethnic_groupgroup D:transport_meansschool_bus -0.9133 4.5777
## ethnic_groupgroup E:transport_meansschool_bus -10.3518 5.0390
## parent_educbachelor's degree:parent_marital_statusmarried -18.4745 6.5736
## parent_educhigh school:parent_marital_statusmarried 0.7418 4.8751
## parent_educmaster's degree:parent_marital_statusmarried 1.1993 6.6521
## parent_educsome college:parent_marital_statusmarried -7.4232 4.9354
## parent_educsome high school:parent_marital_statusmarried -8.2283 4.9536
## parent_educbachelor's degree:parent_marital_statussingle -23.6304 7.4269
## parent_educhigh school:parent_marital_statussingle 1.7141 5.5986
## parent_educmaster's degree:parent_marital_statussingle -0.6344 7.3500
## parent_educsome college:parent_marital_statussingle -11.5881 5.6728
## parent_educsome high school:parent_marital_statussingle -11.5407 5.5591
## parent_educbachelor's degree:parent_marital_statuswidowed -33.5004 17.3280
## parent_educhigh school:parent_marital_statuswidowed -46.5554 20.4448
## parent_educmaster's degree:parent_marital_statuswidowed -48.9590 29.6690
## parent_educsome college:parent_marital_statuswidowed -15.7099 19.0668
## parent_educsome high school:parent_marital_statuswidowed -19.2638 19.6446
## parent_educbachelor's degree:is_first_childyes -3.3589 4.3330
## parent_educhigh school:is_first_childyes 8.9969 3.8002
## parent_educmaster's degree:is_first_childyes 4.7183 5.6364
## parent_educsome college:is_first_childyes 6.6947 3.7542
## parent_educsome high school:is_first_childyes 2.0436 3.7438
## lunch_typestandard:practice_sportregularly 8.4203 4.1608
## lunch_typestandard:practice_sportsometimes 11.3662 4.0244
## lunch_typestandard:transport_meansschool_bus -3.4368 2.4159
## test_prepnone:is_first_childyes -3.6884 2.6012
## test_prepnone:wkly_study_hours> 10 -6.2865 3.6457
## test_prepnone:wkly_study_hours10-May -0.1976 2.8984
## parent_marital_statusmarried:is_first_childyes -8.7047 3.9485
## parent_marital_statussingle:is_first_childyes -1.9060 4.3893
## parent_marital_statuswidowed:is_first_childyes 13.7975 13.4714
## parent_marital_statusmarried:transport_meansschool_bus 7.2707 3.3639
## parent_marital_statussingle:transport_meansschool_bus 2.4715 3.7983
## parent_marital_statuswidowed:transport_meansschool_bus -14.6085 12.8542
## parent_marital_statusmarried:wkly_study_hours> 10 11.6354 5.1480
## parent_marital_statussingle:wkly_study_hours> 10 18.6339 5.7474
## parent_marital_statuswidowed:wkly_study_hours> 10 11.9898 16.7894
## parent_marital_statusmarried:wkly_study_hours10-May 2.1127 3.7866
## parent_marital_statussingle:wkly_study_hours10-May 5.6965 4.2936
## parent_marital_statuswidowed:wkly_study_hours10-May 11.8849 14.3211
## is_first_childyes:transport_meansschool_bus -4.4000 2.5494
## is_first_childyes:wkly_study_hours> 10 -0.6479 3.7705
## is_first_childyes:wkly_study_hours10-May -5.6646 2.8793
## t value Pr(>|t|)
## (Intercept) 5.716 1.84e-08 ***
## gendermale 4.409 1.26e-05 ***
## ethnic_groupgroup B 0.800 0.423863
## ethnic_groupgroup C 1.354 0.176457
## ethnic_groupgroup D 1.239 0.215799
## ethnic_groupgroup E 4.866 1.51e-06 ***
## parent_educbachelor's degree 3.545 0.000428 ***
## parent_educhigh school -2.290 0.022411 *
## parent_educmaster's degree -0.262 0.793302
## parent_educsome college 0.168 0.866672
## parent_educsome high school 0.317 0.751071
## lunch_typestandard 1.468 0.142671
## test_prepnone -0.359 0.719670
## parent_marital_statusmarried 1.779 0.075838 .
## parent_marital_statussingle 0.617 0.537217
## parent_marital_statuswidowed 1.373 0.170360
## practice_sportregularly -1.263 0.207275
## practice_sportsometimes -1.853 0.064470 .
## is_first_childyes 2.299 0.021890 *
## transport_meansschool_bus 0.975 0.329901
## wkly_study_hours> 10 -0.779 0.436602
## wkly_study_hours10-May 1.000 0.317963
## ethnic_groupgroup B:transport_meansschool_bus -0.908 0.364253
## ethnic_groupgroup C:transport_meansschool_bus -1.722 0.085632 .
## ethnic_groupgroup D:transport_meansschool_bus -0.200 0.841936
## ethnic_groupgroup E:transport_meansschool_bus -2.054 0.040440 *
## parent_educbachelor's degree:parent_marital_statusmarried -2.810 0.005133 **
## parent_educhigh school:parent_marital_statusmarried 0.152 0.879115
## parent_educmaster's degree:parent_marital_statusmarried 0.180 0.856998
## parent_educsome college:parent_marital_statusmarried -1.504 0.133168
## parent_educsome high school:parent_marital_statusmarried -1.661 0.097298 .
## parent_educbachelor's degree:parent_marital_statussingle -3.182 0.001551 **
## parent_educhigh school:parent_marital_statussingle 0.306 0.759606
## parent_educmaster's degree:parent_marital_statussingle -0.086 0.931250
## parent_educsome college:parent_marital_statussingle -2.043 0.041580 *
## parent_educsome high school:parent_marital_statussingle -2.076 0.038380 *
## parent_educbachelor's degree:parent_marital_statuswidowed -1.933 0.053737 .
## parent_educhigh school:parent_marital_statuswidowed -2.277 0.023182 *
## parent_educmaster's degree:parent_marital_statuswidowed -1.650 0.099508 .
## parent_educsome college:parent_marital_statuswidowed -0.824 0.410350
## parent_educsome high school:parent_marital_statuswidowed -0.981 0.327238
## parent_educbachelor's degree:is_first_childyes -0.775 0.438573
## parent_educhigh school:is_first_childyes 2.368 0.018271 *
## parent_educmaster's degree:is_first_childyes 0.837 0.402905
## parent_educsome college:is_first_childyes 1.783 0.075121 .
## parent_educsome high school:is_first_childyes 0.546 0.585404
## lunch_typestandard:practice_sportregularly 2.024 0.043509 *
## lunch_typestandard:practice_sportsometimes 2.824 0.004918 **
## lunch_typestandard:transport_meansschool_bus -1.423 0.155457
## test_prepnone:is_first_childyes -1.418 0.156801
## test_prepnone:wkly_study_hours> 10 -1.724 0.085236 .
## test_prepnone:wkly_study_hours10-May -0.068 0.945661
## parent_marital_statusmarried:is_first_childyes -2.205 0.027922 *
## parent_marital_statussingle:is_first_childyes -0.434 0.664285
## parent_marital_statuswidowed:is_first_childyes 1.024 0.306211
## parent_marital_statusmarried:transport_meansschool_bus 2.161 0.031117 *
## parent_marital_statussingle:transport_meansschool_bus 0.651 0.515535
## parent_marital_statuswidowed:transport_meansschool_bus -1.136 0.256279
## parent_marital_statusmarried:wkly_study_hours> 10 2.260 0.024220 *
## parent_marital_statussingle:wkly_study_hours> 10 3.242 0.001262 **
## parent_marital_statuswidowed:wkly_study_hours> 10 0.714 0.475465
## parent_marital_statusmarried:wkly_study_hours10-May 0.558 0.577124
## parent_marital_statussingle:wkly_study_hours10-May 1.327 0.185170
## parent_marital_statuswidowed:wkly_study_hours10-May 0.830 0.406980
## is_first_childyes:transport_meansschool_bus -1.726 0.084951 .
## is_first_childyes:wkly_study_hours> 10 -0.172 0.863627
## is_first_childyes:wkly_study_hours10-May -1.967 0.049669 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.02 on 523 degrees of freedom
## Multiple R-squared: 0.4207, Adjusted R-squared: 0.3476
## F-statistic: 5.755 on 66 and 523 DF, p-value: < 2.2e-16
REading Score
df_4_mdl_read=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,reading_score)
full_fit_read=lm(reading_score ~ .^2,data=df_4_mdl_read)
summary(full_fit_read)
##
## Call:
## lm(formula = reading_score ~ .^2, data = df_4_mdl_read)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.758 -7.294 0.000 7.418 27.742
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 81.321731 17.167189
## gendermale -12.452051 8.746220
## ethnic_groupgroup B -22.239861 14.760619
## ethnic_groupgroup C -29.866442 13.925159
## ethnic_groupgroup D -14.526414 15.158345
## ethnic_groupgroup E -12.302699 14.206212
## parent_educbachelor's degree 33.009059 15.519735
## parent_educhigh school 10.568006 12.847471
## parent_educmaster's degree -24.461817 21.208891
## parent_educsome college -8.316968 12.606066
## parent_educsome high school -4.455992 12.227987
## lunch_typestandard 2.962788 8.683223
## test_prepnone -21.345506 9.059903
## parent_marital_statusmarried 16.095657 11.535602
## parent_marital_statussingle 5.120602 13.883607
## parent_marital_statuswidowed 30.884374 41.015667
## practice_sportregularly -22.428022 13.810663
## practice_sportsometimes -19.634669 13.740867
## is_first_childyes 16.375726 9.948217
## transport_meansschool_bus -1.212990 8.806349
## wkly_study_hours> 10 -17.887902 13.565927
## wkly_study_hours10-May 6.195369 10.901941
## gendermale:ethnic_groupgroup B 7.922999 5.540120
## gendermale:ethnic_groupgroup C 12.191147 5.327795
## gendermale:ethnic_groupgroup D 8.192752 5.292503
## gendermale:ethnic_groupgroup E 9.251399 5.868168
## gendermale:parent_educbachelor's degree -2.815989 4.660163
## gendermale:parent_educhigh school 0.610374 3.800446
## gendermale:parent_educmaster's degree 7.279615 6.524814
## gendermale:parent_educsome college -4.141922 3.991004
## gendermale:parent_educsome high school 1.008352 3.920233
## gendermale:lunch_typestandard -1.073739 2.722340
## gendermale:test_prepnone 0.251653 2.713118
## gendermale:parent_marital_statusmarried -0.523193 3.867655
## gendermale:parent_marital_statussingle -1.745302 4.384747
## gendermale:parent_marital_statuswidowed 1.627846 18.986441
## gendermale:practice_sportregularly -4.310235 4.610325
## gendermale:practice_sportsometimes -3.516087 4.634508
## gendermale:is_first_childyes 3.360372 2.847909
## gendermale:transport_meansschool_bus -0.351231 2.632552
## gendermale:wkly_study_hours> 10 -4.536157 4.129918
## gendermale:wkly_study_hours10-May -1.585990 3.132127
## ethnic_groupgroup B:parent_educbachelor's degree -3.324954 12.924044
## ethnic_groupgroup C:parent_educbachelor's degree -1.783597 12.903276
## ethnic_groupgroup D:parent_educbachelor's degree -4.193155 12.805839
## ethnic_groupgroup E:parent_educbachelor's degree -11.352581 14.573901
## ethnic_groupgroup B:parent_educhigh school -15.455925 8.091351
## ethnic_groupgroup C:parent_educhigh school -8.942855 7.776991
## ethnic_groupgroup D:parent_educhigh school -7.859495 7.906714
## ethnic_groupgroup E:parent_educhigh school -9.368700 8.805485
## ethnic_groupgroup B:parent_educmaster's degree 19.405920 15.527488
## ethnic_groupgroup C:parent_educmaster's degree 4.673731 14.422492
## ethnic_groupgroup D:parent_educmaster's degree 12.168775 14.651954
## ethnic_groupgroup E:parent_educmaster's degree 14.049007 15.416565
## ethnic_groupgroup B:parent_educsome college 4.664900 8.948253
## ethnic_groupgroup C:parent_educsome college 8.349426 8.446297
## ethnic_groupgroup D:parent_educsome college 11.079460 8.797228
## ethnic_groupgroup E:parent_educsome college 8.211551 8.893668
## ethnic_groupgroup B:parent_educsome high school -11.966506 8.576569
## ethnic_groupgroup C:parent_educsome high school -4.495760 8.047085
## ethnic_groupgroup D:parent_educsome high school -3.780939 8.099992
## ethnic_groupgroup E:parent_educsome high school 4.417092 8.696931
## ethnic_groupgroup B:lunch_typestandard 5.652071 5.760897
## ethnic_groupgroup C:lunch_typestandard 10.226437 5.587239
## ethnic_groupgroup D:lunch_typestandard 8.972876 5.499776
## ethnic_groupgroup E:lunch_typestandard 1.828807 6.373559
## ethnic_groupgroup B:test_prepnone 5.358082 5.877498
## ethnic_groupgroup C:test_prepnone 10.226148 5.513504
## ethnic_groupgroup D:test_prepnone 7.509603 5.524539
## ethnic_groupgroup E:test_prepnone 13.877806 6.013663
## ethnic_groupgroup B:parent_marital_statusmarried 7.666966 7.934987
## ethnic_groupgroup C:parent_marital_statusmarried 1.502948 7.306752
## ethnic_groupgroup D:parent_marital_statusmarried -9.884703 7.206665
## ethnic_groupgroup E:parent_marital_statusmarried -0.914626 7.973170
## ethnic_groupgroup B:parent_marital_statussingle 18.560281 9.394771
## ethnic_groupgroup C:parent_marital_statussingle 7.986241 8.882343
## ethnic_groupgroup D:parent_marital_statussingle 3.213487 8.582960
## ethnic_groupgroup E:parent_marital_statussingle 14.967904 9.892795
## ethnic_groupgroup B:parent_marital_statuswidowed 50.612530 105.115426
## ethnic_groupgroup C:parent_marital_statuswidowed 78.991045 85.429965
## ethnic_groupgroup D:parent_marital_statuswidowed 4.650894 86.120208
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 14.613295 10.525698
## ethnic_groupgroup C:practice_sportregularly 14.627286 10.430812
## ethnic_groupgroup D:practice_sportregularly 12.114331 11.643524
## ethnic_groupgroup E:practice_sportregularly 15.486520 10.659168
## ethnic_groupgroup B:practice_sportsometimes 14.385211 11.228160
## ethnic_groupgroup C:practice_sportsometimes 22.578975 10.921110
## ethnic_groupgroup D:practice_sportsometimes 13.257823 12.039573
## ethnic_groupgroup E:practice_sportsometimes 14.799736 10.976620
## ethnic_groupgroup B:is_first_childyes 7.019423 5.832717
## ethnic_groupgroup C:is_first_childyes 0.945600 5.502186
## ethnic_groupgroup D:is_first_childyes -0.578091 5.565974
## ethnic_groupgroup E:is_first_childyes 0.006724 6.269137
## ethnic_groupgroup B:transport_meansschool_bus -9.549492 5.835934
## ethnic_groupgroup C:transport_meansschool_bus -12.156811 5.388780
## ethnic_groupgroup D:transport_meansschool_bus -3.839999 5.383422
## ethnic_groupgroup E:transport_meansschool_bus -11.722753 6.354914
## ethnic_groupgroup B:wkly_study_hours> 10 -8.400227 9.935104
## ethnic_groupgroup C:wkly_study_hours> 10 -0.687654 9.811241
## ethnic_groupgroup D:wkly_study_hours> 10 0.263262 9.797612
## ethnic_groupgroup E:wkly_study_hours> 10 -2.759617 10.673194
## ethnic_groupgroup B:wkly_study_hours10-May -7.860645 8.344055
## ethnic_groupgroup C:wkly_study_hours10-May -2.433650 8.164758
## ethnic_groupgroup D:wkly_study_hours10-May -2.347630 8.302701
## ethnic_groupgroup E:wkly_study_hours10-May -6.220986 8.939387
## parent_educbachelor's degree:lunch_typestandard 0.537231 5.014512
## parent_educhigh school:lunch_typestandard 0.798236 4.046623
## parent_educmaster's degree:lunch_typestandard 6.644511 7.416722
## parent_educsome college:lunch_typestandard 3.328751 4.079308
## parent_educsome high school:lunch_typestandard 5.530921 4.225656
## parent_educbachelor's degree:test_prepnone -2.906807 4.626773
## parent_educhigh school:test_prepnone 2.313360 4.431222
## parent_educmaster's degree:test_prepnone 0.511485 7.888189
## parent_educsome college:test_prepnone -3.095198 4.153258
## parent_educsome high school:test_prepnone 2.618495 4.016780
## parent_educbachelor's degree:parent_marital_statusmarried -18.253458 8.257834
## parent_educhigh school:parent_marital_statusmarried 3.996656 5.807660
## parent_educmaster's degree:parent_marital_statusmarried 0.758405 8.402414
## parent_educsome college:parent_marital_statusmarried -7.340772 5.719024
## parent_educsome high school:parent_marital_statusmarried -4.263094 5.636000
## parent_educbachelor's degree:parent_marital_statussingle -16.758528 8.901756
## parent_educhigh school:parent_marital_statussingle 8.616682 6.344144
## parent_educmaster's degree:parent_marital_statussingle 0.012577 8.969310
## parent_educsome college:parent_marital_statussingle -5.727081 6.369453
## parent_educsome high school:parent_marital_statussingle -1.033222 6.292098
## parent_educbachelor's degree:parent_marital_statuswidowed -21.688307 87.516115
## parent_educhigh school:parent_marital_statuswidowed -57.550419 96.291731
## parent_educmaster's degree:parent_marital_statuswidowed -77.367781 50.441787
## parent_educsome college:parent_marital_statuswidowed -60.045162 63.244771
## parent_educsome high school:parent_marital_statuswidowed -37.108747 75.801849
## parent_educbachelor's degree:practice_sportregularly -3.662981 8.525723
## parent_educhigh school:practice_sportregularly -14.710426 7.337095
## parent_educmaster's degree:practice_sportregularly 1.377177 10.367956
## parent_educsome college:practice_sportregularly -0.382685 7.461303
## parent_educsome high school:practice_sportregularly -3.964045 7.205456
## parent_educbachelor's degree:practice_sportsometimes -12.591005 8.181090
## parent_educhigh school:practice_sportsometimes -11.930485 6.949111
## parent_educmaster's degree:practice_sportsometimes 6.527368 8.636835
## parent_educsome college:practice_sportsometimes 1.040653 7.180635
## parent_educsome high school:practice_sportsometimes 1.496483 6.751679
## parent_educbachelor's degree:is_first_childyes 4.788458 5.062901
## parent_educhigh school:is_first_childyes 6.532806 4.321769
## parent_educmaster's degree:is_first_childyes 6.212508 7.559206
## parent_educsome college:is_first_childyes 9.548352 4.220353
## parent_educsome high school:is_first_childyes 4.792705 4.250326
## parent_educbachelor's degree:transport_meansschool_bus 0.906739 5.054249
## parent_educhigh school:transport_meansschool_bus 3.388782 4.035129
## parent_educmaster's degree:transport_meansschool_bus 4.816803 6.221602
## parent_educsome college:transport_meansschool_bus 3.654650 4.108899
## parent_educsome high school:transport_meansschool_bus 6.032445 4.180954
## parent_educbachelor's degree:wkly_study_hours> 10 -8.191880 7.456993
## parent_educhigh school:wkly_study_hours> 10 -8.343145 6.207418
## parent_educmaster's degree:wkly_study_hours> 10 -1.790263 13.431842
## parent_educsome college:wkly_study_hours> 10 -5.998216 6.248173
## parent_educsome high school:wkly_study_hours> 10 -6.744473 6.363801
## parent_educbachelor's degree:wkly_study_hours10-May -1.946279 5.182903
## parent_educhigh school:wkly_study_hours10-May -10.690295 4.832196
## parent_educmaster's degree:wkly_study_hours10-May -1.124984 6.910172
## parent_educsome college:wkly_study_hours10-May -2.915727 4.920451
## parent_educsome high school:wkly_study_hours10-May -8.675554 5.191456
## lunch_typestandard:test_prepnone -3.365201 3.035153
## lunch_typestandard:parent_marital_statusmarried -7.902908 3.971499
## lunch_typestandard:parent_marital_statussingle -3.707488 4.598623
## lunch_typestandard:parent_marital_statuswidowed 9.372773 78.604395
## lunch_typestandard:practice_sportregularly 6.988929 5.235054
## lunch_typestandard:practice_sportsometimes 10.284128 5.046396
## lunch_typestandard:is_first_childyes -3.701755 3.075286
## lunch_typestandard:transport_meansschool_bus -3.696061 2.822109
## lunch_typestandard:wkly_study_hours> 10 7.910873 4.306472
## lunch_typestandard:wkly_study_hours10-May -0.616925 3.221350
## test_prepnone:parent_marital_statusmarried 3.767046 4.039735
## test_prepnone:parent_marital_statussingle -0.269557 4.650957
## test_prepnone:parent_marital_statuswidowed -33.676919 41.067330
## test_prepnone:practice_sportregularly 2.975412 5.049660
## test_prepnone:practice_sportsometimes 4.627924 4.948802
## test_prepnone:is_first_childyes 1.185331 3.047862
## test_prepnone:transport_meansschool_bus 1.799887 2.771281
## test_prepnone:wkly_study_hours> 10 -2.777623 4.350100
## test_prepnone:wkly_study_hours10-May 1.550628 3.433108
## parent_marital_statusmarried:practice_sportregularly 3.293520 6.491421
## parent_marital_statussingle:practice_sportregularly -4.424243 8.489011
## parent_marital_statuswidowed:practice_sportregularly -6.906882 83.123661
## parent_marital_statusmarried:practice_sportsometimes 1.290178 6.401773
## parent_marital_statussingle:practice_sportsometimes -4.334220 8.299021
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -17.146416 4.775198
## parent_marital_statussingle:is_first_childyes -8.538880 5.292427
## parent_marital_statuswidowed:is_first_childyes 21.917582 29.457760
## parent_marital_statusmarried:transport_meansschool_bus 4.369244 3.943480
## parent_marital_statussingle:transport_meansschool_bus -1.084605 4.494112
## parent_marital_statuswidowed:transport_meansschool_bus -14.288412 19.143923
## parent_marital_statusmarried:wkly_study_hours> 10 21.137631 6.160491
## parent_marital_statussingle:wkly_study_hours> 10 27.104463 6.851117
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 3.638193 4.522464
## parent_marital_statussingle:wkly_study_hours10-May 4.406511 4.994941
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -3.848217 5.864087
## practice_sportsometimes:is_first_childyes -6.246496 5.721937
## practice_sportregularly:transport_meansschool_bus 8.897678 4.900075
## practice_sportsometimes:transport_meansschool_bus 5.610130 4.755946
## practice_sportregularly:wkly_study_hours> 10 4.200015 6.947009
## practice_sportsometimes:wkly_study_hours> 10 3.936511 6.813953
## practice_sportregularly:wkly_study_hours10-May 7.801823 5.346218
## practice_sportsometimes:wkly_study_hours10-May 0.374090 5.271160
## is_first_childyes:transport_meansschool_bus -1.537098 2.982819
## is_first_childyes:wkly_study_hours> 10 2.206912 4.484172
## is_first_childyes:wkly_study_hours10-May -2.954512 3.384923
## transport_meansschool_bus:wkly_study_hours> 10 0.704788 4.309112
## transport_meansschool_bus:wkly_study_hours10-May 2.548938 3.111517
## t value Pr(>|t|)
## (Intercept) 4.737 3.06e-06 ***
## gendermale -1.424 0.155346
## ethnic_groupgroup B -1.507 0.132711
## ethnic_groupgroup C -2.145 0.032599 *
## ethnic_groupgroup D -0.958 0.338510
## ethnic_groupgroup E -0.866 0.387028
## parent_educbachelor's degree 2.127 0.034066 *
## parent_educhigh school 0.823 0.411262
## parent_educmaster's degree -1.153 0.249476
## parent_educsome college -0.660 0.509805
## parent_educsome high school -0.364 0.715753
## lunch_typestandard 0.341 0.733134
## test_prepnone -2.356 0.018974 *
## parent_marital_statusmarried 1.395 0.163733
## parent_marital_statussingle 0.369 0.712463
## parent_marital_statuswidowed 0.753 0.451919
## practice_sportregularly -1.624 0.105206
## practice_sportsometimes -1.429 0.153841
## is_first_childyes 1.646 0.100564
## transport_meansschool_bus -0.138 0.890518
## wkly_study_hours> 10 -1.319 0.188094
## wkly_study_hours10-May 0.568 0.570177
## gendermale:ethnic_groupgroup B 1.430 0.153500
## gendermale:ethnic_groupgroup C 2.288 0.022669 *
## gendermale:ethnic_groupgroup D 1.548 0.122450
## gendermale:ethnic_groupgroup E 1.577 0.115727
## gendermale:parent_educbachelor's degree -0.604 0.546023
## gendermale:parent_educhigh school 0.161 0.872488
## gendermale:parent_educmaster's degree 1.116 0.265258
## gendermale:parent_educsome college -1.038 0.300011
## gendermale:parent_educsome high school 0.257 0.797149
## gendermale:lunch_typestandard -0.394 0.693492
## gendermale:test_prepnone 0.093 0.926147
## gendermale:parent_marital_statusmarried -0.135 0.892466
## gendermale:parent_marital_statussingle -0.398 0.690823
## gendermale:parent_marital_statuswidowed 0.086 0.931720
## gendermale:practice_sportregularly -0.935 0.350424
## gendermale:practice_sportsometimes -0.759 0.448513
## gendermale:is_first_childyes 1.180 0.238755
## gendermale:transport_meansschool_bus -0.133 0.893933
## gendermale:wkly_study_hours> 10 -1.098 0.272735
## gendermale:wkly_study_hours10-May -0.506 0.612894
## ethnic_groupgroup B:parent_educbachelor's degree -0.257 0.797109
## ethnic_groupgroup C:parent_educbachelor's degree -0.138 0.890133
## ethnic_groupgroup D:parent_educbachelor's degree -0.327 0.743513
## ethnic_groupgroup E:parent_educbachelor's degree -0.779 0.436480
## ethnic_groupgroup B:parent_educhigh school -1.910 0.056857 .
## ethnic_groupgroup C:parent_educhigh school -1.150 0.250898
## ethnic_groupgroup D:parent_educhigh school -0.994 0.320837
## ethnic_groupgroup E:parent_educhigh school -1.064 0.288016
## ethnic_groupgroup B:parent_educmaster's degree 1.250 0.212144
## ethnic_groupgroup C:parent_educmaster's degree 0.324 0.746071
## ethnic_groupgroup D:parent_educmaster's degree 0.831 0.406761
## ethnic_groupgroup E:parent_educmaster's degree 0.911 0.362714
## ethnic_groupgroup B:parent_educsome college 0.521 0.602445
## ethnic_groupgroup C:parent_educsome college 0.989 0.323517
## ethnic_groupgroup D:parent_educsome college 1.259 0.208643
## ethnic_groupgroup E:parent_educsome college 0.923 0.356431
## ethnic_groupgroup B:parent_educsome high school -1.395 0.163747
## ethnic_groupgroup C:parent_educsome high school -0.559 0.576705
## ethnic_groupgroup D:parent_educsome high school -0.467 0.640921
## ethnic_groupgroup E:parent_educsome high school 0.508 0.611822
## ethnic_groupgroup B:lunch_typestandard 0.981 0.327158
## ethnic_groupgroup C:lunch_typestandard 1.830 0.067979 .
## ethnic_groupgroup D:lunch_typestandard 1.631 0.103607
## ethnic_groupgroup E:lunch_typestandard 0.287 0.774316
## ethnic_groupgroup B:test_prepnone 0.912 0.362539
## ethnic_groupgroup C:test_prepnone 1.855 0.064401 .
## ethnic_groupgroup D:test_prepnone 1.359 0.174846
## ethnic_groupgroup E:test_prepnone 2.308 0.021547 *
## ethnic_groupgroup B:parent_marital_statusmarried 0.966 0.334542
## ethnic_groupgroup C:parent_marital_statusmarried 0.206 0.837140
## ethnic_groupgroup D:parent_marital_statusmarried -1.372 0.170989
## ethnic_groupgroup E:parent_marital_statusmarried -0.115 0.908733
## ethnic_groupgroup B:parent_marital_statussingle 1.976 0.048918 *
## ethnic_groupgroup C:parent_marital_statussingle 0.899 0.369157
## ethnic_groupgroup D:parent_marital_statussingle 0.374 0.708312
## ethnic_groupgroup E:parent_marital_statussingle 1.513 0.131102
## ethnic_groupgroup B:parent_marital_statuswidowed 0.481 0.630440
## ethnic_groupgroup C:parent_marital_statuswidowed 0.925 0.355741
## ethnic_groupgroup D:parent_marital_statuswidowed 0.054 0.956960
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 1.388 0.165839
## ethnic_groupgroup C:practice_sportregularly 1.402 0.161631
## ethnic_groupgroup D:practice_sportregularly 1.040 0.298794
## ethnic_groupgroup E:practice_sportregularly 1.453 0.147075
## ethnic_groupgroup B:practice_sportsometimes 1.281 0.200908
## ethnic_groupgroup C:practice_sportsometimes 2.067 0.039362 *
## ethnic_groupgroup D:practice_sportsometimes 1.101 0.271507
## ethnic_groupgroup E:practice_sportsometimes 1.348 0.178360
## ethnic_groupgroup B:is_first_childyes 1.203 0.229543
## ethnic_groupgroup C:is_first_childyes 0.172 0.863639
## ethnic_groupgroup D:is_first_childyes -0.104 0.917334
## ethnic_groupgroup E:is_first_childyes 0.001 0.999145
## ethnic_groupgroup B:transport_meansschool_bus -1.636 0.102593
## ethnic_groupgroup C:transport_meansschool_bus -2.256 0.024637 *
## ethnic_groupgroup D:transport_meansschool_bus -0.713 0.476094
## ethnic_groupgroup E:transport_meansschool_bus -1.845 0.065857 .
## ethnic_groupgroup B:wkly_study_hours> 10 -0.846 0.398354
## ethnic_groupgroup C:wkly_study_hours> 10 -0.070 0.944160
## ethnic_groupgroup D:wkly_study_hours> 10 0.027 0.978577
## ethnic_groupgroup E:wkly_study_hours> 10 -0.259 0.796117
## ethnic_groupgroup B:wkly_study_hours10-May -0.942 0.346753
## ethnic_groupgroup C:wkly_study_hours10-May -0.298 0.765813
## ethnic_groupgroup D:wkly_study_hours10-May -0.283 0.777517
## ethnic_groupgroup E:wkly_study_hours10-May -0.696 0.486909
## parent_educbachelor's degree:lunch_typestandard 0.107 0.914738
## parent_educhigh school:lunch_typestandard 0.197 0.843729
## parent_educmaster's degree:lunch_typestandard 0.896 0.370878
## parent_educsome college:lunch_typestandard 0.816 0.415002
## parent_educsome high school:lunch_typestandard 1.309 0.191356
## parent_educbachelor's degree:test_prepnone -0.628 0.530209
## parent_educhigh school:test_prepnone 0.522 0.601931
## parent_educmaster's degree:test_prepnone 0.065 0.948334
## parent_educsome college:test_prepnone -0.745 0.456580
## parent_educsome high school:test_prepnone 0.652 0.514864
## parent_educbachelor's degree:parent_marital_statusmarried -2.210 0.027665 *
## parent_educhigh school:parent_marital_statusmarried 0.688 0.491762
## parent_educmaster's degree:parent_marital_statusmarried 0.090 0.928128
## parent_educsome college:parent_marital_statusmarried -1.284 0.200068
## parent_educsome high school:parent_marital_statusmarried -0.756 0.449872
## parent_educbachelor's degree:parent_marital_statussingle -1.883 0.060511 .
## parent_educhigh school:parent_marital_statussingle 1.358 0.175196
## parent_educmaster's degree:parent_marital_statussingle 0.001 0.998882
## parent_educsome college:parent_marital_statussingle -0.899 0.369139
## parent_educsome high school:parent_marital_statussingle -0.164 0.869653
## parent_educbachelor's degree:parent_marital_statuswidowed -0.248 0.804406
## parent_educhigh school:parent_marital_statuswidowed -0.598 0.550415
## parent_educmaster's degree:parent_marital_statuswidowed -1.534 0.125904
## parent_educsome college:parent_marital_statuswidowed -0.949 0.343011
## parent_educsome high school:parent_marital_statuswidowed -0.490 0.624733
## parent_educbachelor's degree:practice_sportregularly -0.430 0.667700
## parent_educhigh school:practice_sportregularly -2.005 0.045673 *
## parent_educmaster's degree:practice_sportregularly 0.133 0.894397
## parent_educsome college:practice_sportregularly -0.051 0.959122
## parent_educsome high school:practice_sportregularly -0.550 0.582541
## parent_educbachelor's degree:practice_sportsometimes -1.539 0.124621
## parent_educhigh school:practice_sportsometimes -1.717 0.086818 .
## parent_educmaster's degree:practice_sportsometimes 0.756 0.450258
## parent_educsome college:practice_sportsometimes 0.145 0.884846
## parent_educsome high school:practice_sportsometimes 0.222 0.824708
## parent_educbachelor's degree:is_first_childyes 0.946 0.344850
## parent_educhigh school:is_first_childyes 1.512 0.131459
## parent_educmaster's degree:is_first_childyes 0.822 0.411676
## parent_educsome college:is_first_childyes 2.262 0.024229 *
## parent_educsome high school:is_first_childyes 1.128 0.260191
## parent_educbachelor's degree:transport_meansschool_bus 0.179 0.857717
## parent_educhigh school:transport_meansschool_bus 0.840 0.401533
## parent_educmaster's degree:transport_meansschool_bus 0.774 0.439287
## parent_educsome college:transport_meansschool_bus 0.889 0.374321
## parent_educsome high school:transport_meansschool_bus 1.443 0.149883
## parent_educbachelor's degree:wkly_study_hours> 10 -1.099 0.272654
## parent_educhigh school:wkly_study_hours> 10 -1.344 0.179724
## parent_educmaster's degree:wkly_study_hours> 10 -0.133 0.894038
## parent_educsome college:wkly_study_hours> 10 -0.960 0.337663
## parent_educsome high school:wkly_study_hours> 10 -1.060 0.289895
## parent_educbachelor's degree:wkly_study_hours10-May -0.376 0.707482
## parent_educhigh school:wkly_study_hours10-May -2.212 0.027535 *
## parent_educmaster's degree:wkly_study_hours10-May -0.163 0.870761
## parent_educsome college:wkly_study_hours10-May -0.593 0.553816
## parent_educsome high school:wkly_study_hours10-May -1.671 0.095514 .
## lunch_typestandard:test_prepnone -1.109 0.268237
## lunch_typestandard:parent_marital_statusmarried -1.990 0.047312 *
## lunch_typestandard:parent_marital_statussingle -0.806 0.420618
## lunch_typestandard:parent_marital_statuswidowed 0.119 0.905148
## lunch_typestandard:practice_sportregularly 1.335 0.182661
## lunch_typestandard:practice_sportsometimes 2.038 0.042245 *
## lunch_typestandard:is_first_childyes -1.204 0.229445
## lunch_typestandard:transport_meansschool_bus -1.310 0.191089
## lunch_typestandard:wkly_study_hours> 10 1.837 0.066989 .
## lunch_typestandard:wkly_study_hours10-May -0.192 0.848226
## test_prepnone:parent_marital_statusmarried 0.932 0.351667
## test_prepnone:parent_marital_statussingle -0.058 0.953813
## test_prepnone:parent_marital_statuswidowed -0.820 0.412702
## test_prepnone:practice_sportregularly 0.589 0.556054
## test_prepnone:practice_sportsometimes 0.935 0.350295
## test_prepnone:is_first_childyes 0.389 0.697562
## test_prepnone:transport_meansschool_bus 0.649 0.516419
## test_prepnone:wkly_study_hours> 10 -0.639 0.523517
## test_prepnone:wkly_study_hours10-May 0.452 0.651763
## parent_marital_statusmarried:practice_sportregularly 0.507 0.612191
## parent_marital_statussingle:practice_sportregularly -0.521 0.602548
## parent_marital_statuswidowed:practice_sportregularly -0.083 0.933822
## parent_marital_statusmarried:practice_sportsometimes 0.202 0.840388
## parent_marital_statussingle:practice_sportsometimes -0.522 0.601793
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -3.591 0.000373 ***
## parent_marital_statussingle:is_first_childyes -1.613 0.107478
## parent_marital_statuswidowed:is_first_childyes 0.744 0.457312
## parent_marital_statusmarried:transport_meansschool_bus 1.108 0.268571
## parent_marital_statussingle:transport_meansschool_bus -0.241 0.809421
## parent_marital_statuswidowed:transport_meansschool_bus -0.746 0.455903
## parent_marital_statusmarried:wkly_study_hours> 10 3.431 0.000666 ***
## parent_marital_statussingle:wkly_study_hours> 10 3.956 9.07e-05 ***
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 0.804 0.421624
## parent_marital_statussingle:wkly_study_hours10-May 0.882 0.378225
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -0.656 0.512067
## practice_sportsometimes:is_first_childyes -1.092 0.275662
## practice_sportregularly:transport_meansschool_bus 1.816 0.070179 .
## practice_sportsometimes:transport_meansschool_bus 1.180 0.238890
## practice_sportregularly:wkly_study_hours> 10 0.605 0.545817
## practice_sportsometimes:wkly_study_hours> 10 0.578 0.563797
## practice_sportregularly:wkly_study_hours10-May 1.459 0.145298
## practice_sportsometimes:wkly_study_hours10-May 0.071 0.943459
## is_first_childyes:transport_meansschool_bus -0.515 0.606629
## is_first_childyes:wkly_study_hours> 10 0.492 0.622891
## is_first_childyes:wkly_study_hours10-May -0.873 0.383295
## transport_meansschool_bus:wkly_study_hours> 10 0.164 0.870166
## transport_meansschool_bus:wkly_study_hours10-May 0.819 0.413185
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.87 on 383 degrees of freedom
## Multiple R-squared: 0.5303, Adjusted R-squared: 0.2777
## F-statistic: 2.099 on 206 and 383 DF, p-value: 2.19e-10
stepwise_model_read <- step(full_fit_read, direction = "both", trace = 1)
## Start: AIC=3174.13
## reading_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours)^2
##
## Df Sum of Sq RSS AIC
## - ethnic_group:wkly_study_hours 8 614.8 64084 3163.8
## - parent_educ:wkly_study_hours 10 1420.6 64890 3167.2
## - parent_educ:transport_means 5 415.6 63885 3168.0
## - ethnic_group:parent_educ 20 3769.8 67239 3168.2
## - parent_educ:lunch_type 5 448.1 63918 3168.3
## - parent_educ:test_prep 5 452.4 63922 3168.3
## - gender:parent_marital_status 3 36.6 63506 3168.5
## - parent_marital_status:practice_sport 4 295.7 63765 3168.9
## - gender:parent_educ 5 629.0 64099 3170.0
## - transport_means:wkly_study_hours 2 123.0 63593 3171.3
## - gender:practice_sport 2 145.0 63615 3171.5
## - test_prep:practice_sport 2 164.3 63634 3171.7
## - ethnic_group:is_first_child 4 609.4 64079 3171.8
## - gender:wkly_study_hours 2 202.8 63672 3172.0
## - gender:test_prep 1 1.4 63471 3172.1
## - gender:transport_means 1 2.9 63473 3172.2
## - test_prep:is_first_child 1 25.1 63495 3172.4
## - gender:lunch_type 1 25.8 63495 3172.4
## - test_prep:wkly_study_hours 2 242.4 63712 3172.4
## - parent_educ:is_first_child 5 899.0 64369 3172.4
## - is_first_child:transport_means 1 44.0 63514 3172.5
## - practice_sport:is_first_child 2 259.9 63730 3172.5
## - test_prep:transport_means 1 69.9 63539 3172.8
## - is_first_child:wkly_study_hours 2 322.5 63792 3173.1
## - test_prep:parent_marital_status 2 337.8 63807 3173.3
## - parent_educ:parent_marital_status 13 2799.2 66269 3173.6
## - lunch_type:test_prep 1 203.7 63673 3174.0
## <none> 63470 3174.1
## - gender:is_first_child 1 230.7 63700 3174.3
## - lunch_type:is_first_child 1 240.1 63710 3174.4
## - parent_marital_status:transport_means 3 678.8 64148 3174.4
## - ethnic_group:practice_sport 8 1798.4 65268 3174.6
## - gender:ethnic_group 4 933.4 64403 3174.7
## - lunch_type:transport_means 1 284.2 63754 3174.8
## - ethnic_group:lunch_type 4 995.4 64465 3175.3
## - practice_sport:transport_means 2 595.4 64065 3175.6
## - ethnic_group:test_prep 4 1172.3 64642 3176.9
## - lunch_type:practice_sport 2 753.7 64223 3177.1
## - lunch_type:parent_marital_status 2 780.0 64250 3177.3
## - practice_sport:wkly_study_hours 4 1228.1 64698 3177.4
## - parent_educ:practice_sport 10 2564.7 66034 3177.5
## - lunch_type:wkly_study_hours 2 855.7 64325 3178.0
## - ethnic_group:transport_means 4 1492.9 64962 3179.9
## - ethnic_group:parent_marital_status 9 2935.6 66405 3182.8
## - parent_marital_status:wkly_study_hours 4 2936.1 66406 3192.8
## - parent_marital_status:is_first_child 2 2728.2 66198 3195.0
##
## Step: AIC=3163.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:wkly_study_hours + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_educ 20 3674.5 67759 3156.7
## - parent_educ:transport_means 5 373.1 64458 3157.2
## - parent_marital_status:practice_sport 4 207.2 64292 3157.7
## - parent_educ:test_prep 5 437.9 64522 3157.8
## - parent_educ:wkly_study_hours 10 1542.6 65627 3157.9
## - parent_educ:lunch_type 5 440.6 64525 3157.9
## - gender:parent_marital_status 3 40.5 64125 3158.2
## - gender:parent_educ 5 657.6 64742 3159.8
## - transport_means:wkly_study_hours 2 68.6 64153 3160.5
## - gender:wkly_study_hours 2 148.7 64233 3161.2
## - gender:practice_sport 2 163.3 64248 3161.3
## - ethnic_group:is_first_child 4 606.3 64691 3161.4
## - test_prep:practice_sport 2 177.1 64261 3161.4
## - gender:transport_means 1 1.5 64086 3161.8
## - parent_educ:parent_marital_status 13 2664.0 66748 3161.9
## - test_prep:is_first_child 1 10.1 64094 3161.9
## - gender:test_prep 1 11.1 64095 3161.9
## - gender:lunch_type 1 32.7 64117 3162.1
## - test_prep:wkly_study_hours 2 253.0 64337 3162.1
## - parent_educ:is_first_child 5 914.6 64999 3162.2
## - is_first_child:transport_means 1 51.4 64136 3162.3
## - practice_sport:is_first_child 2 272.2 64357 3162.3
## - test_prep:transport_means 1 62.9 64147 3162.4
## - test_prep:parent_marital_status 2 349.0 64433 3163.0
## - lunch_type:test_prep 1 162.2 64247 3163.3
## - is_first_child:wkly_study_hours 2 382.1 64467 3163.3
## - gender:is_first_child 1 171.5 64256 3163.4
## <none> 64084 3163.8
## - gender:ethnic_group 4 876.2 64961 3163.8
## - ethnic_group:practice_sport 8 1783.4 65868 3164.0
## - lunch_type:is_first_child 1 255.0 64339 3164.2
## - lunch_type:transport_means 1 257.3 64342 3164.2
## - parent_marital_status:transport_means 3 747.2 64832 3164.7
## - practice_sport:transport_means 2 575.9 64660 3165.1
## - ethnic_group:lunch_type 4 1030.9 65115 3165.2
## - parent_educ:practice_sport 10 2521.2 66606 3166.6
## - lunch_type:practice_sport 2 747.6 64832 3166.7
## - lunch_type:parent_marital_status 2 764.2 64849 3166.8
## - ethnic_group:test_prep 4 1220.5 65305 3167.0
## - practice_sport:wkly_study_hours 4 1277.6 65362 3167.5
## - lunch_type:wkly_study_hours 2 896.1 64981 3168.0
## - ethnic_group:transport_means 4 1568.2 65653 3170.1
## - ethnic_group:parent_marital_status 9 2898.4 66983 3171.9
## + ethnic_group:wkly_study_hours 8 614.8 63470 3174.1
## - parent_marital_status:wkly_study_hours 4 2786.9 66871 3180.9
## - parent_marital_status:is_first_child 2 2661.3 66746 3183.8
##
## Step: AIC=3156.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:wkly_study_hours + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 1269.9 69029 3147.7
## - parent_educ:test_prep 5 307.0 68066 3149.4
## - parent_educ:lunch_type 5 386.5 68145 3150.1
## - parent_educ:transport_means 5 461.7 68221 3150.7
## - parent_marital_status:practice_sport 4 242.6 68001 3150.8
## - gender:parent_marital_status 3 138.7 67898 3151.9
## - ethnic_group:practice_sport 8 1348.4 69107 3152.3
## - gender:parent_educ 5 701.3 68460 3152.8
## - parent_educ:is_first_child 5 840.6 68600 3154.0
## - transport_means:wkly_study_hours 2 158.4 67917 3154.1
## - test_prep:practice_sport 2 181.0 67940 3154.3
## - gender:wkly_study_hours 2 187.1 67946 3154.3
## - is_first_child:wkly_study_hours 2 193.0 67952 3154.4
## - practice_sport:is_first_child 2 209.8 67969 3154.5
## - parent_educ:practice_sport 10 2091.0 69850 3154.6
## - test_prep:is_first_child 1 0.0 67759 3154.7
## - gender:lunch_type 1 1.5 67760 3154.7
## - gender:transport_means 1 6.0 67765 3154.8
## - gender:test_prep 1 28.8 67788 3155.0
## - is_first_child:transport_means 1 31.9 67791 3155.0
## - lunch_type:test_prep 1 39.0 67798 3155.1
## - gender:is_first_child 1 53.7 67813 3155.2
## - gender:practice_sport 2 289.5 68048 3155.2
## - parent_marital_status:transport_means 3 527.4 68286 3155.3
## - test_prep:wkly_study_hours 2 299.0 68058 3155.3
## - lunch_type:parent_marital_status 2 301.2 68060 3155.3
## - ethnic_group:is_first_child 4 776.5 68535 3155.4
## - test_prep:transport_means 1 93.8 67853 3155.5
## - test_prep:parent_marital_status 2 332.4 68091 3155.6
## - parent_educ:parent_marital_status 13 2982.5 70741 3156.1
## - gender:ethnic_group 4 905.4 68664 3156.5
## - practice_sport:transport_means 2 445.2 68204 3156.6
## <none> 67759 3156.7
## - lunch_type:is_first_child 1 315.4 68074 3157.5
## - lunch_type:transport_means 1 316.6 68076 3157.5
## - ethnic_group:test_prep 4 1135.3 68894 3158.5
## - ethnic_group:lunch_type 4 1174.9 68934 3158.9
## - practice_sport:wkly_study_hours 4 1254.5 69013 3159.5
## - lunch_type:practice_sport 2 898.1 68657 3160.5
## - ethnic_group:transport_means 4 1420.9 69180 3161.0
## - lunch_type:wkly_study_hours 2 1153.6 68912 3162.7
## + ethnic_group:parent_educ 20 3674.5 64084 3163.8
## - ethnic_group:parent_marital_status 9 2958.5 70717 3163.9
## - parent_marital_status:wkly_study_hours 4 2214.9 69974 3167.7
## + ethnic_group:wkly_study_hours 8 519.5 67239 3168.2
## - parent_marital_status:is_first_child 2 2405.1 70164 3173.3
##
## Step: AIC=3147.67
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:lunch_type 5 320.2 69349 3140.4
## - parent_educ:test_prep 5 383.5 69412 3140.9
## - parent_marital_status:practice_sport 4 281.9 69311 3142.1
## - parent_educ:transport_means 5 536.0 69565 3142.2
## - gender:parent_marital_status 3 108.9 69138 3142.6
## - ethnic_group:practice_sport 8 1371.2 70400 3143.3
## - gender:parent_educ 5 719.3 69748 3143.8
## - parent_educ:is_first_child 5 751.8 69781 3144.1
## - is_first_child:wkly_study_hours 2 140.8 69170 3144.9
## - transport_means:wkly_study_hours 2 190.3 69219 3145.3
## - practice_sport:is_first_child 2 196.8 69226 3145.4
## - test_prep:practice_sport 2 233.3 69262 3145.7
## - test_prep:is_first_child 1 0.2 69029 3145.7
## - gender:transport_means 1 0.3 69029 3145.7
## - gender:lunch_type 1 3.0 69032 3145.7
## - gender:practice_sport 2 243.8 69273 3145.8
## - lunch_type:test_prep 1 17.2 69046 3145.8
## - gender:test_prep 1 29.3 69058 3145.9
## - is_first_child:transport_means 1 45.0 69074 3146.1
## - gender:is_first_child 1 76.7 69106 3146.3
## - gender:wkly_study_hours 2 313.2 69342 3146.3
## - parent_marital_status:transport_means 3 553.7 69582 3146.4
## - test_prep:parent_marital_status 2 325.4 69354 3146.4
## - test_prep:transport_means 1 96.8 69126 3146.5
## - lunch_type:parent_marital_status 2 332.8 69362 3146.5
## - practice_sport:transport_means 2 339.7 69369 3146.6
## - ethnic_group:is_first_child 4 835.0 69864 3146.8
## - test_prep:wkly_study_hours 2 400.0 69429 3147.1
## - gender:ethnic_group 4 886.0 69915 3147.2
## - parent_educ:practice_sport 10 2344.8 71374 3147.4
## <none> 69029 3147.7
## - lunch_type:is_first_child 1 244.1 69273 3147.8
## - ethnic_group:lunch_type 4 956.4 69985 3147.8
## - practice_sport:wkly_study_hours 4 1068.0 70097 3148.7
## - lunch_type:transport_means 1 366.9 69396 3148.8
## - parent_educ:parent_marital_status 13 3281.5 72310 3149.1
## - ethnic_group:test_prep 4 1108.8 70138 3149.1
## - lunch_type:practice_sport 2 846.3 69875 3150.9
## - ethnic_group:transport_means 4 1324.6 70353 3150.9
## - lunch_type:wkly_study_hours 2 1037.5 70066 3152.5
## - ethnic_group:parent_marital_status 9 3215.7 72244 3156.5
## + parent_educ:wkly_study_hours 10 1269.9 67759 3156.7
## + ethnic_group:parent_educ 20 3401.8 65627 3157.9
## + ethnic_group:wkly_study_hours 8 590.3 68439 3158.6
## - parent_marital_status:wkly_study_hours 4 2375.7 71404 3159.6
## - parent_marital_status:is_first_child 2 2553.3 71582 3165.1
##
## Step: AIC=3140.4
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:test_prep 5 341.0 69690 3133.3
## - parent_marital_status:practice_sport 4 306.4 69655 3135.0
## - parent_educ:transport_means 5 558.5 69908 3135.1
## - ethnic_group:practice_sport 8 1291.4 70640 3135.3
## - gender:parent_marital_status 3 130.7 69480 3135.5
## - gender:parent_educ 5 692.2 70041 3136.3
## - parent_educ:is_first_child 5 738.5 70088 3136.7
## - is_first_child:wkly_study_hours 2 148.9 69498 3137.7
## - practice_sport:is_first_child 2 212.5 69561 3138.2
## - transport_means:wkly_study_hours 2 223.6 69573 3138.3
## - gender:transport_means 1 0.1 69349 3138.4
## - test_prep:is_first_child 1 1.4 69350 3138.4
## - gender:practice_sport 2 240.3 69589 3138.4
## - gender:lunch_type 1 11.3 69360 3138.5
## - lunch_type:test_prep 1 17.1 69366 3138.6
## - test_prep:practice_sport 2 258.3 69607 3138.6
## - gender:test_prep 1 32.6 69382 3138.7
## - is_first_child:transport_means 1 42.2 69391 3138.8
## - gender:wkly_study_hours 2 292.4 69641 3138.9
## - lunch_type:parent_marital_status 2 322.6 69672 3139.1
## - test_prep:parent_marital_status 2 339.4 69688 3139.3
## - test_prep:transport_means 1 110.2 69459 3139.3
## - gender:is_first_child 1 123.4 69472 3139.4
## - parent_marital_status:transport_means 3 609.9 69959 3139.6
## - ethnic_group:is_first_child 4 848.6 70198 3139.6
## - gender:ethnic_group 4 857.9 70207 3139.7
## - test_prep:wkly_study_hours 2 403.6 69753 3139.8
## - practice_sport:transport_means 2 407.8 69757 3139.9
## - lunch_type:is_first_child 1 218.0 69567 3140.3
## <none> 69349 3140.4
## - ethnic_group:lunch_type 4 951.4 70300 3140.4
## - parent_educ:practice_sport 10 2413.6 71763 3140.6
## - lunch_type:transport_means 1 377.6 69727 3141.6
## - practice_sport:wkly_study_hours 4 1124.5 70474 3141.9
## - ethnic_group:test_prep 4 1131.5 70481 3141.9
## - parent_educ:parent_marital_status 13 3369.7 72719 3142.4
## - lunch_type:practice_sport 2 809.1 70158 3143.2
## - ethnic_group:transport_means 4 1299.6 70649 3143.4
## - lunch_type:wkly_study_hours 2 993.1 70342 3144.8
## + parent_educ:lunch_type 5 320.2 69029 3147.7
## - ethnic_group:parent_marital_status 9 3147.4 72496 3148.6
## + parent_educ:wkly_study_hours 10 1203.6 68145 3150.1
## + ethnic_group:parent_educ 20 3421.3 65928 3150.6
## + ethnic_group:wkly_study_hours 8 565.0 68784 3151.6
## - parent_marital_status:wkly_study_hours 4 2520.8 71870 3153.5
## - parent_marital_status:is_first_child 2 2752.7 72102 3159.4
##
## Step: AIC=3133.3
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:practice_sport 4 317.6 70008 3128.0
## - ethnic_group:practice_sport 8 1274.2 70964 3128.0
## - gender:parent_marital_status 3 123.8 69814 3128.3
## - gender:parent_educ 5 652.4 70342 3128.8
## - parent_educ:transport_means 5 667.2 70357 3128.9
## - parent_educ:is_first_child 5 796.7 70487 3130.0
## - is_first_child:wkly_study_hours 2 124.6 69815 3130.3
## - practice_sport:is_first_child 2 200.9 69891 3131.0
## - transport_means:wkly_study_hours 2 208.5 69899 3131.1
## - gender:practice_sport 2 223.7 69914 3131.2
## - test_prep:practice_sport 2 229.3 69919 3131.2
## - test_prep:is_first_child 1 0.3 69690 3131.3
## - gender:transport_means 1 1.0 69691 3131.3
## - gender:lunch_type 1 8.7 69699 3131.4
## - lunch_type:test_prep 1 19.1 69709 3131.5
## - lunch_type:parent_marital_status 2 264.9 69955 3131.5
## - gender:ethnic_group 4 753.5 70444 3131.6
## - gender:test_prep 1 55.9 69746 3131.8
## - test_prep:parent_marital_status 2 301.2 69991 3131.8
## - is_first_child:transport_means 1 67.9 69758 3131.9
## - gender:wkly_study_hours 2 310.5 70001 3131.9
## - test_prep:transport_means 1 100.3 69790 3132.2
## - gender:is_first_child 1 104.9 69795 3132.2
## - parent_marital_status:transport_means 3 587.6 70278 3132.2
## - ethnic_group:is_first_child 4 907.0 70597 3132.9
## - practice_sport:transport_means 2 436.3 70126 3133.0
## - test_prep:wkly_study_hours 2 443.2 70133 3133.0
## <none> 69690 3133.3
## - ethnic_group:test_prep 4 951.6 70642 3133.3
## - lunch_type:is_first_child 1 248.8 69939 3133.4
## - parent_educ:practice_sport 10 2425.2 72115 3133.5
## - ethnic_group:lunch_type 4 1002.5 70692 3133.7
## - lunch_type:transport_means 1 375.0 70065 3134.5
## - parent_educ:parent_marital_status 13 3343.7 73034 3134.9
## - practice_sport:wkly_study_hours 4 1153.2 70843 3135.0
## - ethnic_group:transport_means 4 1310.7 71001 3136.3
## - lunch_type:practice_sport 2 917.5 70608 3137.0
## - lunch_type:wkly_study_hours 2 1061.6 70752 3138.2
## + parent_educ:test_prep 5 341.0 69349 3140.4
## - ethnic_group:parent_marital_status 9 3065.0 72755 3140.7
## + parent_educ:lunch_type 5 277.8 69412 3140.9
## + parent_educ:wkly_study_hours 10 1255.7 68434 3142.6
## + ethnic_group:wkly_study_hours 8 565.8 69124 3144.5
## + ethnic_group:parent_educ 20 3212.4 66478 3145.4
## - parent_marital_status:wkly_study_hours 4 2684.2 72374 3147.6
## - parent_marital_status:is_first_child 2 2781.2 72471 3152.4
##
## Step: AIC=3127.98
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 122.7 70130 3123.0
## - ethnic_group:practice_sport 8 1365.0 71373 3123.4
## - gender:parent_educ 5 663.1 70671 3123.5
## - parent_educ:transport_means 5 690.2 70698 3123.8
## - lunch_type:parent_marital_status 3 322.0 70330 3124.7
## - parent_educ:is_first_child 5 800.9 70809 3124.7
## - practice_sport:is_first_child 2 150.9 70159 3125.2
## - is_first_child:wkly_study_hours 2 163.9 70172 3125.4
## - transport_means:wkly_study_hours 2 204.8 70212 3125.7
## - test_prep:practice_sport 2 236.5 70244 3126.0
## - gender:ethnic_group 4 714.8 70722 3126.0
## - test_prep:is_first_child 1 0.6 70008 3126.0
## - gender:transport_means 1 1.9 70010 3126.0
## - gender:lunch_type 1 7.2 70015 3126.0
## - lunch_type:test_prep 1 18.2 70026 3126.1
## - gender:practice_sport 2 264.3 70272 3126.2
## - test_prep:parent_marital_status 2 280.5 70288 3126.3
## - gender:test_prep 1 66.7 70074 3126.5
## - is_first_child:transport_means 1 87.2 70095 3126.7
## - test_prep:transport_means 1 93.7 70101 3126.8
## - gender:is_first_child 1 97.3 70105 3126.8
## - gender:wkly_study_hours 2 342.9 70351 3126.9
## - parent_marital_status:transport_means 3 583.7 70591 3126.9
## - practice_sport:transport_means 2 401.2 70409 3127.3
## - lunch_type:is_first_child 1 177.5 70185 3127.5
## - ethnic_group:is_first_child 4 929.5 70937 3127.8
## - ethnic_group:test_prep 4 940.7 70948 3127.9
## - test_prep:wkly_study_hours 2 463.2 70471 3127.9
## <none> 70008 3128.0
## - parent_educ:practice_sport 10 2449.6 72457 3128.3
## - lunch_type:transport_means 1 337.8 70345 3128.8
## - parent_educ:parent_marital_status 14 3565.4 73573 3129.3
## - ethnic_group:lunch_type 4 1115.6 71123 3129.3
## - practice_sport:wkly_study_hours 4 1150.0 71158 3129.6
## - ethnic_group:transport_means 4 1283.9 71292 3130.7
## - lunch_type:practice_sport 2 877.2 70885 3131.3
## - lunch_type:wkly_study_hours 2 1099.1 71107 3133.2
## + parent_marital_status:practice_sport 4 317.6 69690 3133.3
## - ethnic_group:parent_marital_status 10 3190.9 73199 3134.3
## + parent_educ:test_prep 5 352.3 69655 3135.0
## + parent_educ:lunch_type 5 297.6 69710 3135.5
## + parent_educ:wkly_study_hours 10 1290.0 68718 3137.0
## + ethnic_group:wkly_study_hours 8 481.0 69527 3139.9
## + ethnic_group:parent_educ 20 3249.9 66758 3139.9
## - parent_marital_status:wkly_study_hours 5 2853.2 72861 3141.6
## - parent_marital_status:is_first_child 2 3039.8 73048 3149.1
##
## Step: AIC=3123.01
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:practice_sport 8 1356.7 71487 3118.3
## - gender:parent_educ 5 677.1 70808 3118.7
## - parent_educ:transport_means 5 685.0 70815 3118.8
## - parent_educ:is_first_child 5 819.9 70950 3119.9
## - lunch_type:parent_marital_status 3 369.0 70499 3120.1
## - practice_sport:is_first_child 2 144.7 70275 3120.2
## - is_first_child:wkly_study_hours 2 152.6 70283 3120.3
## - transport_means:wkly_study_hours 2 204.9 70335 3120.7
## - gender:ethnic_group 4 700.0 70830 3120.9
## - test_prep:is_first_child 1 0.5 70131 3121.0
## - gender:transport_means 1 1.0 70131 3121.0
## - gender:lunch_type 1 4.8 70135 3121.1
## - lunch_type:test_prep 1 21.6 70152 3121.2
## - test_prep:practice_sport 2 266.1 70396 3121.2
## - gender:practice_sport 2 277.7 70408 3121.3
## - test_prep:parent_marital_status 2 280.8 70411 3121.4
## - gender:test_prep 1 80.0 70210 3121.7
## - test_prep:transport_means 1 91.3 70222 3121.8
## - is_first_child:transport_means 1 113.9 70244 3122.0
## - gender:is_first_child 1 114.3 70245 3122.0
## - gender:wkly_study_hours 2 363.0 70493 3122.1
## - practice_sport:transport_means 2 389.5 70520 3122.3
## - parent_marital_status:transport_means 3 660.2 70791 3122.5
## - lunch_type:is_first_child 1 183.4 70314 3122.6
## - ethnic_group:is_first_child 4 913.5 71044 3122.7
## - test_prep:wkly_study_hours 2 455.4 70586 3122.8
## - ethnic_group:test_prep 4 952.9 71083 3123.0
## <none> 70130 3123.0
## - parent_educ:parent_marital_status 14 3455.4 73586 3123.4
## - lunch_type:transport_means 1 356.3 70487 3124.0
## - ethnic_group:lunch_type 4 1108.7 71239 3124.3
## - parent_educ:practice_sport 10 2585.2 72716 3124.4
## - practice_sport:wkly_study_hours 4 1194.7 71325 3125.0
## - ethnic_group:transport_means 4 1264.1 71395 3125.6
## - lunch_type:practice_sport 2 959.8 71090 3127.0
## + gender:parent_marital_status 3 122.7 70008 3128.0
## - lunch_type:wkly_study_hours 2 1110.6 71241 3128.3
## + parent_marital_status:practice_sport 4 316.5 69814 3128.3
## - ethnic_group:parent_marital_status 10 3250.3 73381 3129.7
## + parent_educ:test_prep 5 345.4 69785 3130.1
## + parent_educ:lunch_type 5 315.8 69815 3130.3
## + parent_educ:wkly_study_hours 10 1252.2 68878 3132.4
## + ethnic_group:parent_educ 20 3339.0 66791 3134.2
## + ethnic_group:wkly_study_hours 8 511.2 69619 3134.7
## - parent_marital_status:wkly_study_hours 5 2844.3 72975 3136.5
## - parent_marital_status:is_first_child 2 3138.1 73269 3144.8
##
## Step: AIC=3118.32
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:transport_means 5 548.5 72036 3112.8
## - gender:parent_educ 5 581.6 72069 3113.1
## - gender:ethnic_group 4 534.8 72022 3114.7
## - practice_sport:is_first_child 2 121.8 71609 3115.3
## - lunch_type:parent_marital_status 3 394.4 71882 3115.6
## - is_first_child:wkly_study_hours 2 177.5 71665 3115.8
## - test_prep:practice_sport 2 196.3 71683 3115.9
## - parent_educ:is_first_child 5 939.4 72427 3116.0
## - transport_means:wkly_study_hours 2 221.2 71708 3116.1
## - lunch_type:test_prep 1 0.0 71487 3116.3
## - gender:lunch_type 1 0.1 71487 3116.3
## - gender:transport_means 1 0.3 71487 3116.3
## - test_prep:is_first_child 1 0.7 71488 3116.3
## - gender:test_prep 1 50.9 71538 3116.7
## - gender:is_first_child 1 53.6 71541 3116.8
## - test_prep:parent_marital_status 2 313.1 71800 3116.9
## - ethnic_group:is_first_child 4 825.4 72313 3117.1
## - test_prep:wkly_study_hours 2 338.3 71825 3117.1
## - test_prep:transport_means 1 106.9 71594 3117.2
## - practice_sport:transport_means 2 376.1 71863 3117.4
## - is_first_child:transport_means 1 164.3 71651 3117.7
## - ethnic_group:test_prep 4 919.2 72406 3117.9
## - gender:practice_sport 2 453.1 71940 3118.1
## <none> 71487 3118.3
## - gender:wkly_study_hours 2 487.4 71974 3118.3
## - lunch_type:is_first_child 1 245.8 71733 3118.3
## - lunch_type:transport_means 1 258.5 71746 3118.4
## - parent_educ:parent_marital_status 14 3522.4 75010 3118.7
## - parent_marital_status:transport_means 3 781.1 72268 3118.7
## - parent_educ:practice_sport 10 2650.7 74138 3119.8
## - practice_sport:wkly_study_hours 4 1180.8 72668 3120.0
## - ethnic_group:lunch_type 4 1274.7 72762 3120.8
## - ethnic_group:transport_means 4 1324.6 72812 3121.2
## - lunch_type:practice_sport 2 969.1 72456 3122.3
## + parent_marital_status:practice_sport 4 402.2 71085 3123.0
## + ethnic_group:practice_sport 8 1356.7 70130 3123.0
## - lunch_type:wkly_study_hours 2 1089.7 72577 3123.2
## + gender:parent_marital_status 3 114.4 71373 3123.4
## - ethnic_group:parent_marital_status 10 3370.4 74858 3125.5
## + parent_educ:test_prep 5 312.5 71175 3125.7
## + parent_educ:lunch_type 5 224.8 71262 3126.5
## + parent_educ:wkly_study_hours 10 1304.6 70182 3127.4
## + ethnic_group:wkly_study_hours 8 473.3 71014 3130.4
## - parent_marital_status:wkly_study_hours 5 2938.9 74426 3132.1
## + ethnic_group:parent_educ 20 2867.8 68619 3134.2
## - parent_marital_status:is_first_child 2 2933.5 74421 3138.1
##
## Step: AIC=3112.83
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_educ 5 603.8 72639 3107.8
## - gender:ethnic_group 4 475.9 72512 3108.7
## - practice_sport:is_first_child 2 88.0 72124 3109.6
## - is_first_child:wkly_study_hours 2 178.3 72214 3110.3
## - test_prep:practice_sport 2 197.3 72233 3110.4
## - lunch_type:parent_marital_status 3 454.7 72490 3110.5
## - parent_educ:is_first_child 5 958.0 72994 3110.6
## - transport_means:wkly_study_hours 2 234.3 72270 3110.7
## - gender:transport_means 1 0.0 72036 3110.8
## - test_prep:is_first_child 1 0.9 72036 3110.8
## - gender:lunch_type 1 1.7 72037 3110.8
## - lunch_type:test_prep 1 2.7 72038 3110.8
## - gender:test_prep 1 37.7 72073 3111.1
## - test_prep:parent_marital_status 2 287.2 72323 3111.2
## - gender:is_first_child 1 49.1 72085 3111.2
## - practice_sport:transport_means 2 304.8 72340 3111.3
## - test_prep:wkly_study_hours 2 352.0 72388 3111.7
## - is_first_child:transport_means 1 135.0 72171 3111.9
## - ethnic_group:is_first_child 4 874.0 72910 3111.9
## - test_prep:transport_means 1 146.1 72182 3112.0
## - parent_marital_status:transport_means 3 668.1 72704 3112.3
## - gender:wkly_study_hours 2 433.5 72469 3112.4
## - parent_educ:parent_marital_status 14 3444.3 75480 3112.4
## - ethnic_group:test_prep 4 945.8 72981 3112.5
## - gender:practice_sport 2 458.7 72494 3112.6
## - lunch_type:is_first_child 1 235.4 72271 3112.8
## <none> 72036 3112.8
## - lunch_type:transport_means 1 251.0 72287 3112.9
## - parent_educ:practice_sport 10 2633.4 74669 3114.0
## - practice_sport:wkly_study_hours 4 1297.2 73333 3115.4
## - ethnic_group:lunch_type 4 1387.9 73424 3116.1
## - ethnic_group:transport_means 4 1456.2 73492 3116.6
## - lunch_type:practice_sport 2 986.4 73022 3116.8
## + parent_marital_status:practice_sport 4 414.6 71621 3117.4
## + gender:parent_marital_status 3 109.2 71926 3117.9
## + parent_educ:transport_means 5 548.5 71487 3118.3
## - lunch_type:wkly_study_hours 2 1169.8 73205 3118.3
## + ethnic_group:practice_sport 8 1220.2 70815 3118.8
## + parent_educ:test_prep 5 395.4 71640 3119.6
## - ethnic_group:parent_marital_status 10 3435.4 75471 3120.3
## + parent_educ:lunch_type 5 241.7 71794 3120.8
## + parent_educ:wkly_study_hours 10 1335.5 70700 3121.8
## + ethnic_group:wkly_study_hours 8 495.2 71540 3124.8
## - parent_marital_status:wkly_study_hours 5 3004.4 75040 3126.9
## + ethnic_group:parent_educ 20 3017.4 69018 3127.6
## - parent_marital_status:is_first_child 2 2981.2 75017 3132.8
##
## Step: AIC=3107.75
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:lunch_type + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:ethnic_group 4 357.5 72997 3102.7
## - parent_educ:is_first_child 5 838.9 73478 3104.5
## - practice_sport:is_first_child 2 105.8 72745 3104.6
## - lunch_type:parent_marital_status 3 422.0 73061 3105.2
## - is_first_child:wkly_study_hours 2 205.4 72845 3105.4
## - transport_means:wkly_study_hours 2 231.0 72870 3105.6
## - gender:transport_means 1 0.0 72639 3105.8
## - gender:lunch_type 1 1.4 72641 3105.8
## - test_prep:is_first_child 1 4.8 72644 3105.8
## - lunch_type:test_prep 1 11.0 72650 3105.8
## - test_prep:practice_sport 2 260.4 72900 3105.9
## - test_prep:parent_marital_status 2 267.3 72907 3105.9
## - gender:test_prep 1 27.3 72667 3106.0
## - practice_sport:transport_means 2 287.5 72927 3106.1
## - gender:is_first_child 1 46.8 72686 3106.1
## - ethnic_group:test_prep 4 856.3 73496 3106.7
## - ethnic_group:is_first_child 4 858.1 73497 3106.7
## - is_first_child:transport_means 1 127.0 72766 3106.8
## - test_prep:transport_means 1 128.8 72768 3106.8
## - test_prep:wkly_study_hours 2 412.9 73052 3107.1
## - gender:wkly_study_hours 2 454.8 73094 3107.4
## - gender:practice_sport 2 463.1 73103 3107.5
## - lunch_type:is_first_child 1 216.9 72856 3107.5
## - parent_marital_status:transport_means 3 724.1 73363 3107.6
## <none> 72639 3107.8
## - parent_educ:practice_sport 10 2551.6 75191 3108.1
## - lunch_type:transport_means 1 333.5 72973 3108.5
## - parent_educ:parent_marital_status 14 3774.3 76414 3109.6
## - practice_sport:wkly_study_hours 4 1233.1 73872 3109.7
## - ethnic_group:lunch_type 4 1289.5 73929 3110.1
## - lunch_type:practice_sport 2 942.3 73582 3111.4
## + parent_marital_status:practice_sport 4 431.9 72207 3112.2
## - ethnic_group:transport_means 4 1600.7 74240 3112.6
## + gender:parent_educ 5 603.8 72036 3112.8
## + gender:parent_marital_status 3 108.8 72531 3112.9
## - lunch_type:wkly_study_hours 2 1157.9 73797 3113.1
## + parent_educ:transport_means 5 570.6 72069 3113.1
## - ethnic_group:parent_marital_status 10 3305.3 75945 3114.0
## + ethnic_group:practice_sport 8 1130.0 71509 3114.5
## + parent_educ:test_prep 5 351.2 72288 3114.9
## + parent_educ:lunch_type 5 235.7 72404 3115.8
## + parent_educ:wkly_study_hours 10 1314.3 71325 3117.0
## + ethnic_group:wkly_study_hours 8 515.2 72124 3119.6
## + ethnic_group:parent_educ 20 3119.5 69520 3121.9
## - parent_marital_status:wkly_study_hours 5 3076.4 75716 3122.2
## - parent_marital_status:is_first_child 2 2985.7 75625 3127.5
##
## Step: AIC=3102.65
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:is_first_child 2 121.5 73118 3099.6
## - lunch_type:parent_marital_status 3 402.0 73399 3099.9
## - is_first_child:wkly_study_hours 2 204.6 73201 3100.3
## - parent_educ:is_first_child 5 960.2 73957 3100.4
## - ethnic_group:test_prep 4 712.7 73710 3100.4
## - transport_means:wkly_study_hours 2 234.6 73231 3100.5
## - gender:lunch_type 1 0.3 72997 3100.7
## - gender:transport_means 1 1.6 72998 3100.7
## - test_prep:parent_marital_status 2 250.2 73247 3100.7
## - test_prep:is_first_child 1 5.9 73003 3100.7
## - test_prep:practice_sport 2 258.1 73255 3100.7
## - lunch_type:test_prep 1 18.8 73016 3100.8
## - gender:test_prep 1 19.3 73016 3100.8
## - practice_sport:transport_means 2 282.8 73280 3100.9
## - gender:is_first_child 1 55.7 73052 3101.1
## - ethnic_group:is_first_child 4 838.1 73835 3101.4
## - test_prep:transport_means 1 135.7 73132 3101.7
## - is_first_child:transport_means 1 147.7 73145 3101.8
## - test_prep:wkly_study_hours 2 417.8 73415 3102.0
## - gender:practice_sport 2 467.7 73465 3102.4
## - lunch_type:is_first_child 1 223.6 73220 3102.4
## <none> 72997 3102.7
## - gender:wkly_study_hours 2 497.9 73495 3102.7
## - parent_marital_status:transport_means 3 785.6 73782 3103.0
## - parent_educ:practice_sport 10 2563.4 75560 3103.0
## - lunch_type:transport_means 1 326.1 73323 3103.3
## - ethnic_group:lunch_type 4 1273.0 74270 3104.8
## - practice_sport:wkly_study_hours 4 1285.8 74283 3104.9
## - parent_educ:parent_marital_status 14 3916.8 76914 3105.5
## - lunch_type:practice_sport 2 1063.9 74061 3107.2
## + parent_marital_status:practice_sport 4 401.1 72596 3107.4
## - ethnic_group:transport_means 4 1601.0 74598 3107.4
## - ethnic_group:parent_marital_status 10 3170.2 76167 3107.7
## + gender:ethnic_group 4 357.5 72639 3107.8
## + gender:parent_marital_status 3 100.5 72896 3107.8
## - lunch_type:wkly_study_hours 2 1180.5 74177 3108.1
## + parent_educ:transport_means 5 515.8 72481 3108.5
## + gender:parent_educ 5 485.3 72512 3108.7
## + ethnic_group:practice_sport 8 1051.0 71946 3110.1
## + parent_educ:test_prep 5 256.9 72740 3110.6
## + parent_educ:lunch_type 5 226.0 72771 3110.8
## + parent_educ:wkly_study_hours 10 1282.6 71714 3112.2
## + ethnic_group:wkly_study_hours 8 491.4 72505 3114.7
## - parent_marital_status:wkly_study_hours 5 3086.2 76083 3117.1
## + ethnic_group:parent_educ 20 3022.3 69974 3117.7
## - parent_marital_status:is_first_child 2 3076.4 76073 3123.0
##
## Step: AIC=3099.63
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:parent_marital_status 3 374.8 73493 3096.7
## - is_first_child:wkly_study_hours 2 186.9 73305 3097.1
## - parent_educ:is_first_child 5 949.9 74068 3097.2
## - ethnic_group:test_prep 4 732.4 73851 3097.5
## - transport_means:wkly_study_hours 2 238.0 73356 3097.6
## - test_prep:parent_marital_status 2 246.9 73365 3097.6
## - gender:lunch_type 1 0.3 73119 3097.6
## - test_prep:is_first_child 1 1.5 73120 3097.6
## - gender:transport_means 1 2.9 73121 3097.7
## - lunch_type:test_prep 1 23.0 73141 3097.8
## - practice_sport:transport_means 2 271.5 73390 3097.8
## - gender:test_prep 1 24.4 73143 3097.8
## - test_prep:practice_sport 2 282.1 73400 3097.9
## - gender:is_first_child 1 66.2 73184 3098.2
## - ethnic_group:is_first_child 4 870.1 73988 3098.6
## - test_prep:transport_means 1 138.4 73257 3098.8
## - test_prep:wkly_study_hours 2 402.6 73521 3098.9
## - is_first_child:transport_means 1 164.6 73283 3099.0
## - gender:practice_sport 2 455.9 73574 3099.3
## - gender:wkly_study_hours 2 489.8 73608 3099.6
## - lunch_type:is_first_child 1 245.7 73364 3099.6
## - parent_marital_status:transport_means 3 746.7 73865 3099.6
## <none> 73118 3099.6
## - parent_educ:practice_sport 10 2528.0 75646 3099.7
## - lunch_type:transport_means 1 326.5 73445 3100.3
## - ethnic_group:lunch_type 4 1294.0 74412 3102.0
## - parent_educ:parent_marital_status 14 3861.6 76980 3102.0
## - practice_sport:wkly_study_hours 4 1302.5 74421 3102.1
## + practice_sport:is_first_child 2 121.5 72997 3102.7
## - ethnic_group:transport_means 4 1550.5 74669 3104.0
## - lunch_type:practice_sport 2 1065.3 74184 3104.2
## - ethnic_group:parent_marital_status 10 3109.3 76228 3104.2
## + gender:ethnic_group 4 373.1 72745 3104.6
## + parent_marital_status:practice_sport 4 367.7 72751 3104.7
## + gender:parent_marital_status 3 88.8 73030 3104.9
## - lunch_type:wkly_study_hours 2 1188.6 74307 3105.1
## + gender:parent_educ 5 501.0 72617 3105.6
## + parent_educ:transport_means 5 474.9 72643 3105.8
## + ethnic_group:practice_sport 8 1036.1 72082 3107.2
## + parent_educ:test_prep 5 245.0 72873 3107.7
## + parent_educ:lunch_type 5 228.7 72890 3107.8
## + parent_educ:wkly_study_hours 10 1277.4 71841 3109.2
## + ethnic_group:wkly_study_hours 8 505.9 72612 3111.5
## - parent_marital_status:wkly_study_hours 5 3089.3 76208 3114.1
## + ethnic_group:parent_educ 20 2920.9 70197 3115.6
## - parent_marital_status:is_first_child 2 3028.3 76147 3119.6
##
## Step: AIC=3096.65
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:is_first_child 5 908.9 74402 3093.9
## - is_first_child:wkly_study_hours 2 173.4 73667 3094.0
## - test_prep:parent_marital_status 2 234.7 73728 3094.5
## - test_prep:is_first_child 1 1.1 73494 3094.7
## - ethnic_group:test_prep 4 753.5 74247 3094.7
## - gender:lunch_type 1 6.4 73500 3094.7
## - gender:transport_means 1 6.7 73500 3094.7
## - lunch_type:test_prep 1 20.6 73514 3094.8
## - practice_sport:transport_means 2 273.6 73767 3094.8
## - transport_means:wkly_study_hours 2 274.4 73767 3094.8
## - gender:test_prep 1 35.5 73529 3094.9
## - test_prep:practice_sport 2 290.9 73784 3095.0
## - ethnic_group:is_first_child 4 829.3 74322 3095.3
## - gender:is_first_child 1 81.0 73574 3095.3
## - test_prep:transport_means 1 136.1 73629 3095.7
## - test_prep:wkly_study_hours 2 402.3 73895 3095.9
## - gender:practice_sport 2 412.2 73905 3095.9
## - is_first_child:transport_means 1 175.2 73668 3096.1
## - gender:wkly_study_hours 2 431.3 73924 3096.1
## - lunch_type:is_first_child 1 218.5 73712 3096.4
## - parent_marital_status:transport_means 3 743.8 74237 3096.6
## <none> 73493 3096.7
## - parent_educ:practice_sport 10 2548.8 76042 3096.8
## - lunch_type:transport_means 1 328.3 73821 3097.3
## - practice_sport:wkly_study_hours 4 1295.6 74789 3099.0
## - parent_educ:parent_marital_status 14 3920.7 77414 3099.3
## + lunch_type:parent_marital_status 3 374.8 73118 3099.6
## - ethnic_group:lunch_type 4 1393.2 74886 3099.7
## + practice_sport:is_first_child 2 94.3 73399 3099.9
## - lunch_type:practice_sport 2 998.0 74491 3100.6
## - ethnic_group:parent_marital_status 10 3049.2 76542 3100.6
## - ethnic_group:transport_means 4 1542.9 75036 3100.9
## - lunch_type:wkly_study_hours 2 1093.4 74587 3101.4
## + gender:parent_marital_status 3 124.4 73369 3101.7
## + gender:ethnic_group 4 351.9 73141 3101.8
## + parent_educ:transport_means 5 521.3 72972 3102.4
## + gender:parent_educ 5 479.0 73014 3102.8
## + parent_marital_status:practice_sport 5 428.2 73065 3103.2
## + ethnic_group:practice_sport 8 1039.1 72454 3104.2
## + parent_educ:lunch_type 5 221.6 73272 3104.9
## + parent_educ:test_prep 5 214.7 73278 3104.9
## + parent_educ:wkly_study_hours 10 1282.2 72211 3106.3
## + ethnic_group:wkly_study_hours 8 478.5 73015 3108.8
## - parent_marital_status:wkly_study_hours 5 2984.5 76478 3110.1
## + ethnic_group:parent_educ 20 2625.3 70868 3115.2
## - parent_marital_status:is_first_child 2 3010.8 76504 3116.3
##
## Step: AIC=3093.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - is_first_child:wkly_study_hours 2 116.1 74518 3090.8
## - test_prep:parent_marital_status 2 216.2 74618 3091.6
## - test_prep:is_first_child 1 1.0 74403 3091.9
## - gender:transport_means 1 2.7 74405 3091.9
## - gender:lunch_type 1 4.7 74407 3091.9
## - transport_means:wkly_study_hours 2 263.8 74666 3092.0
## - ethnic_group:test_prep 4 772.1 75174 3092.0
## - lunch_type:test_prep 1 14.6 74417 3092.0
## - practice_sport:transport_means 2 278.7 74681 3092.1
## - gender:test_prep 1 36.6 74439 3092.2
## - ethnic_group:is_first_child 4 820.4 75222 3092.4
## - parent_marital_status:transport_means 3 608.0 75010 3092.7
## - gender:is_first_child 1 113.6 74516 3092.8
## - test_prep:transport_means 1 159.0 74561 3093.2
## - test_prep:practice_sport 2 417.4 74819 3093.2
## - gender:wkly_study_hours 2 418.8 74821 3093.2
## - test_prep:wkly_study_hours 2 435.0 74837 3093.3
## - is_first_child:transport_means 1 223.9 74626 3093.7
## - gender:practice_sport 2 478.2 74880 3093.7
## - lunch_type:is_first_child 1 250.2 74652 3093.9
## <none> 74402 3093.9
## - lunch_type:transport_means 1 305.0 74707 3094.3
## - parent_educ:practice_sport 10 2677.4 77079 3094.8
## - practice_sport:wkly_study_hours 4 1145.4 75547 3094.9
## - parent_educ:parent_marital_status 14 3963.2 78365 3096.5
## + parent_educ:is_first_child 5 908.9 73493 3096.7
## - ethnic_group:lunch_type 4 1401.7 75804 3096.9
## - ethnic_group:parent_marital_status 10 2988.4 77390 3097.1
## + practice_sport:is_first_child 2 89.6 74312 3097.2
## + lunch_type:parent_marital_status 3 333.8 74068 3097.2
## - lunch_type:wkly_study_hours 2 987.7 75390 3097.7
## - lunch_type:practice_sport 2 1005.9 75408 3097.8
## + gender:ethnic_group 4 468.2 73934 3098.2
## - ethnic_group:transport_means 4 1592.6 75995 3098.4
## + gender:parent_marital_status 3 140.4 74262 3098.8
## + parent_educ:transport_means 5 540.0 73862 3099.6
## + parent_marital_status:practice_sport 5 445.6 73956 3100.3
## + gender:parent_educ 5 357.5 74045 3101.1
## + ethnic_group:practice_sport 8 1093.6 73308 3101.2
## + parent_educ:test_prep 5 283.3 74119 3101.7
## + parent_educ:lunch_type 5 216.9 74185 3102.2
## + parent_educ:wkly_study_hours 10 1215.8 73186 3104.2
## + ethnic_group:wkly_study_hours 8 490.9 73911 3106.0
## - parent_marital_status:wkly_study_hours 5 2913.7 77316 3106.6
## - parent_marital_status:is_first_child 2 2779.0 77181 3111.5
## + ethnic_group:parent_educ 20 2651.5 71751 3112.5
##
## Step: AIC=3090.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:parent_marital_status 2 226.9 74745 3088.6
## - ethnic_group:test_prep 4 755.2 75273 3088.8
## - test_prep:is_first_child 1 3.6 74522 3088.8
## - gender:lunch_type 1 4.0 74522 3088.8
## - gender:transport_means 1 5.2 74523 3088.9
## - lunch_type:test_prep 1 20.2 74538 3089.0
## - transport_means:wkly_study_hours 2 276.9 74795 3089.0
## - practice_sport:transport_means 2 283.8 74802 3089.1
## - gender:test_prep 1 39.9 74558 3089.1
## - parent_marital_status:transport_means 3 560.5 75079 3089.2
## - gender:is_first_child 1 131.9 74650 3089.9
## - test_prep:practice_sport 2 389.2 74907 3089.9
## - ethnic_group:is_first_child 4 902.5 75421 3089.9
## - gender:wkly_study_hours 2 420.9 74939 3090.1
## - test_prep:transport_means 1 178.7 74697 3090.2
## - test_prep:wkly_study_hours 2 447.6 74966 3090.3
## - is_first_child:transport_means 1 207.2 74725 3090.5
## - gender:practice_sport 2 487.0 75005 3090.7
## <none> 74518 3090.8
## - lunch_type:is_first_child 1 281.2 74799 3091.0
## - lunch_type:transport_means 1 316.1 74834 3091.3
## - parent_educ:practice_sport 10 2637.3 77155 3091.3
## - practice_sport:wkly_study_hours 4 1218.6 75737 3092.4
## - ethnic_group:parent_marital_status 10 2949.1 77467 3093.7
## + is_first_child:wkly_study_hours 2 116.1 74402 3093.9
## - ethnic_group:lunch_type 4 1419.2 75937 3093.9
## + parent_educ:is_first_child 5 851.5 73667 3094.0
## + practice_sport:is_first_child 2 79.9 74438 3094.2
## - parent_educ:parent_marital_status 14 4073.8 78592 3094.2
## + lunch_type:parent_marital_status 3 325.4 74193 3094.2
## - lunch_type:wkly_study_hours 2 1008.5 75527 3094.8
## - ethnic_group:transport_means 4 1571.5 76090 3095.1
## + gender:ethnic_group 4 463.4 74055 3095.1
## - lunch_type:practice_sport 2 1106.6 75625 3095.5
## + gender:parent_marital_status 3 122.9 74395 3095.8
## + parent_educ:transport_means 5 533.4 73985 3096.6
## + parent_marital_status:practice_sport 5 480.3 74038 3097.0
## + gender:parent_educ 5 382.2 74136 3097.8
## + ethnic_group:practice_sport 8 1106.0 73412 3098.0
## + parent_educ:test_prep 5 252.5 74266 3098.8
## + parent_educ:lunch_type 5 226.9 74291 3099.0
## + parent_educ:wkly_study_hours 10 1196.3 73322 3101.3
## + ethnic_group:wkly_study_hours 8 531.7 73986 3102.6
## - parent_marital_status:wkly_study_hours 5 2935.4 77454 3103.6
## - parent_marital_status:is_first_child 2 2749.1 77267 3108.2
## + ethnic_group:parent_educ 20 2507.0 72011 3110.6
##
## Step: AIC=3088.61
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:is_first_child 1 0.0 74745 3086.6
## - gender:transport_means 1 3.1 74748 3086.6
## - gender:lunch_type 1 3.2 74748 3086.6
## - ethnic_group:test_prep 4 771.7 75517 3086.7
## - lunch_type:test_prep 1 19.0 74764 3086.8
## - transport_means:wkly_study_hours 2 274.1 75019 3086.8
## - practice_sport:transport_means 2 282.2 75027 3086.8
## - gender:test_prep 1 33.7 74779 3086.9
## - parent_marital_status:transport_means 3 637.6 75383 3087.6
## - gender:is_first_child 1 140.0 74885 3087.7
## - gender:wkly_study_hours 2 427.7 75173 3088.0
## - test_prep:practice_sport 2 430.9 75176 3088.0
## - test_prep:wkly_study_hours 2 443.8 75189 3088.1
## - is_first_child:transport_means 1 194.2 74939 3088.1
## - test_prep:transport_means 1 204.7 74950 3088.2
## - gender:practice_sport 2 473.1 75218 3088.3
## - ethnic_group:is_first_child 4 989.3 75734 3088.4
## <none> 74745 3088.6
## - lunch_type:is_first_child 1 262.7 75008 3088.7
## - parent_educ:practice_sport 10 2614.3 77359 3088.9
## - lunch_type:transport_means 1 313.3 75058 3089.1
## - ethnic_group:parent_marital_status 11 2935.6 77681 3089.3
## - parent_educ:parent_marital_status 15 4085.3 78830 3090.0
## - practice_sport:wkly_study_hours 4 1210.8 75956 3090.1
## + test_prep:parent_marital_status 2 226.9 74518 3090.8
## + is_first_child:wkly_study_hours 2 126.8 74618 3091.6
## + parent_educ:is_first_child 5 831.9 73913 3092.0
## + practice_sport:is_first_child 2 75.7 74669 3092.0
## - ethnic_group:lunch_type 4 1478.6 76224 3092.2
## + lunch_type:parent_marital_status 3 308.8 74436 3092.2
## - lunch_type:wkly_study_hours 2 1020.1 75765 3092.6
## - lunch_type:practice_sport 2 1054.2 75799 3092.9
## + gender:ethnic_group 4 446.6 74298 3093.1
## - ethnic_group:transport_means 4 1611.0 76356 3093.2
## + gender:parent_marital_status 3 127.1 74618 3093.6
## + parent_educ:transport_means 5 508.2 74237 3094.6
## + parent_marital_status:practice_sport 5 478.0 74267 3094.8
## + ethnic_group:practice_sport 8 1145.2 73600 3095.5
## + gender:parent_educ 5 370.5 74374 3095.7
## + parent_educ:lunch_type 5 254.2 74491 3096.6
## + parent_educ:test_prep 5 216.4 74529 3096.9
## + parent_educ:wkly_study_hours 10 1231.3 73514 3098.8
## + ethnic_group:wkly_study_hours 8 555.6 74189 3100.2
## - parent_marital_status:wkly_study_hours 6 3151.7 77897 3101.0
## - parent_marital_status:is_first_child 3 2970.8 77716 3105.6
## + ethnic_group:parent_educ 20 2580.0 72165 3107.9
##
## Step: AIC=3086.61
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 3.1 74748 3084.6
## - gender:lunch_type 1 3.2 74748 3084.6
## - ethnic_group:test_prep 4 773.4 75518 3084.7
## - lunch_type:test_prep 1 19.0 74764 3084.8
## - transport_means:wkly_study_hours 2 274.3 75019 3084.8
## - practice_sport:transport_means 2 282.1 75027 3084.8
## - gender:test_prep 1 33.7 74779 3084.9
## - parent_marital_status:transport_means 3 638.4 75383 3085.6
## - gender:is_first_child 1 140.6 74886 3085.7
## - gender:wkly_study_hours 2 429.3 75174 3086.0
## - test_prep:practice_sport 2 431.0 75176 3086.0
## - test_prep:wkly_study_hours 2 443.8 75189 3086.1
## - is_first_child:transport_means 1 194.3 74939 3086.1
## - test_prep:transport_means 1 204.7 74950 3086.2
## - gender:practice_sport 2 474.3 75219 3086.3
## - ethnic_group:is_first_child 4 990.3 75735 3086.4
## <none> 74745 3086.6
## - lunch_type:is_first_child 1 263.8 75009 3086.7
## - parent_educ:practice_sport 10 2614.7 77360 3086.9
## - lunch_type:transport_means 1 315.2 75060 3087.1
## - ethnic_group:parent_marital_status 11 2937.1 77682 3087.3
## - parent_educ:parent_marital_status 15 4085.4 78830 3088.0
## - practice_sport:wkly_study_hours 4 1213.1 75958 3088.1
## + test_prep:is_first_child 1 0.0 74745 3088.6
## + test_prep:parent_marital_status 2 223.3 74522 3088.8
## + is_first_child:wkly_study_hours 2 126.2 74619 3089.6
## + practice_sport:is_first_child 2 75.4 74670 3090.0
## + parent_educ:is_first_child 5 828.7 73916 3090.0
## + lunch_type:parent_marital_status 3 308.7 74436 3090.2
## - ethnic_group:lunch_type 4 1481.4 76226 3090.2
## - lunch_type:wkly_study_hours 2 1020.8 75766 3090.6
## - lunch_type:practice_sport 2 1055.5 75800 3090.9
## + gender:ethnic_group 4 446.6 74298 3091.1
## - ethnic_group:transport_means 4 1611.0 76356 3091.2
## + gender:parent_marital_status 3 126.9 74618 3091.6
## + parent_educ:transport_means 5 504.6 74240 3092.6
## + parent_marital_status:practice_sport 5 478.0 74267 3092.8
## + ethnic_group:practice_sport 8 1145.0 73600 3093.5
## + gender:parent_educ 5 369.4 74376 3093.7
## + parent_educ:lunch_type 5 254.2 74491 3094.6
## + parent_educ:test_prep 5 216.1 74529 3094.9
## + parent_educ:wkly_study_hours 10 1230.4 73515 3096.8
## + ethnic_group:wkly_study_hours 8 552.7 74192 3098.2
## - parent_marital_status:wkly_study_hours 6 3152.6 77898 3099.0
## - parent_marital_status:is_first_child 3 2971.0 77716 3103.6
## + ethnic_group:parent_educ 20 2568.1 72177 3106.0
##
## Step: AIC=3084.64
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 3.4 74751 3082.7
## - ethnic_group:test_prep 4 772.2 75520 3082.7
## - lunch_type:test_prep 1 19.4 74767 3082.8
## - transport_means:wkly_study_hours 2 274.4 75022 3082.8
## - practice_sport:transport_means 2 282.4 75030 3082.9
## - gender:test_prep 1 32.1 74780 3082.9
## - parent_marital_status:transport_means 3 637.5 75386 3083.7
## - gender:is_first_child 1 140.3 74888 3083.7
## - test_prep:practice_sport 2 430.3 75178 3084.0
## - gender:wkly_study_hours 2 430.5 75179 3084.0
## - test_prep:wkly_study_hours 2 443.4 75191 3084.1
## - is_first_child:transport_means 1 197.9 74946 3084.2
## - test_prep:transport_means 1 209.1 74957 3084.3
## - gender:practice_sport 2 476.3 75224 3084.4
## - ethnic_group:is_first_child 4 991.8 75740 3084.4
## <none> 74748 3084.6
## - lunch_type:is_first_child 1 261.5 75010 3084.7
## - parent_educ:practice_sport 10 2633.2 77381 3085.1
## - lunch_type:transport_means 1 319.1 75067 3085.2
## - ethnic_group:parent_marital_status 11 2959.1 77707 3085.5
## - parent_educ:parent_marital_status 15 4087.6 78836 3086.1
## - practice_sport:wkly_study_hours 4 1210.0 75958 3086.1
## + gender:transport_means 1 3.1 74745 3086.6
## + test_prep:is_first_child 1 0.0 74748 3086.6
## + test_prep:parent_marital_status 2 221.4 74527 3086.9
## + is_first_child:wkly_study_hours 2 128.0 74620 3087.6
## + practice_sport:is_first_child 2 76.0 74672 3088.0
## + parent_educ:is_first_child 5 823.7 73924 3088.1
## + lunch_type:parent_marital_status 3 311.0 74437 3088.2
## - ethnic_group:lunch_type 4 1480.1 76228 3088.2
## - lunch_type:wkly_study_hours 2 1018.3 75766 3088.6
## - lunch_type:practice_sport 2 1052.9 75801 3088.9
## + gender:ethnic_group 4 449.4 74299 3089.1
## - ethnic_group:transport_means 4 1611.1 76359 3089.2
## + gender:parent_marital_status 3 126.5 74622 3089.6
## + parent_educ:transport_means 5 503.5 74245 3090.7
## + parent_marital_status:practice_sport 5 479.0 74269 3090.8
## + ethnic_group:practice_sport 8 1137.2 73611 3091.6
## + gender:parent_educ 5 368.6 74379 3091.7
## + parent_educ:lunch_type 5 256.9 74491 3092.6
## + parent_educ:test_prep 5 215.5 74533 3092.9
## + parent_educ:wkly_study_hours 10 1202.3 73546 3095.1
## + ethnic_group:wkly_study_hours 8 551.9 74196 3096.3
## - parent_marital_status:wkly_study_hours 6 3151.6 77900 3097.0
## - parent_marital_status:is_first_child 3 2984.7 77733 3101.7
## + ethnic_group:parent_educ 20 2567.4 72181 3104.0
##
## Step: AIC=3082.66
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:test_prep 4 771.6 75523 3080.7
## - transport_means:wkly_study_hours 2 273.4 75025 3080.8
## - lunch_type:test_prep 1 20.5 74772 3080.8
## - practice_sport:transport_means 2 284.4 75036 3080.9
## - gender:test_prep 1 31.3 74783 3080.9
## - parent_marital_status:transport_means 3 636.2 75388 3081.7
## - gender:is_first_child 1 140.5 74892 3081.8
## - gender:wkly_study_hours 2 428.0 75179 3082.0
## - test_prep:practice_sport 2 433.4 75185 3082.1
## - test_prep:wkly_study_hours 2 443.5 75195 3082.2
## - is_first_child:transport_means 1 195.4 74947 3082.2
## - test_prep:transport_means 1 211.2 74963 3082.3
## - gender:practice_sport 2 475.6 75227 3082.4
## - ethnic_group:is_first_child 4 989.2 75741 3082.4
## <none> 74751 3082.7
## - lunch_type:is_first_child 1 264.5 75016 3082.8
## - parent_educ:practice_sport 10 2629.9 77381 3083.1
## - lunch_type:transport_means 1 323.5 75075 3083.2
## - ethnic_group:parent_marital_status 11 2960.2 77712 3083.6
## - parent_educ:parent_marital_status 15 4086.7 78838 3084.1
## - practice_sport:wkly_study_hours 4 1215.8 75967 3084.2
## + gender:lunch_type 1 3.4 74748 3084.6
## + gender:transport_means 1 3.2 74748 3084.6
## + test_prep:is_first_child 1 0.0 74751 3084.7
## + test_prep:parent_marital_status 2 220.7 74531 3084.9
## + is_first_child:wkly_study_hours 2 127.3 74624 3085.7
## + practice_sport:is_first_child 2 74.4 74677 3086.1
## + parent_educ:is_first_child 5 822.7 73929 3086.1
## + lunch_type:parent_marital_status 3 314.3 74437 3086.2
## - ethnic_group:lunch_type 4 1480.8 76232 3086.2
## - lunch_type:wkly_study_hours 2 1015.8 75767 3086.6
## - lunch_type:practice_sport 2 1077.3 75829 3087.1
## + gender:ethnic_group 4 446.2 74305 3087.1
## - ethnic_group:transport_means 4 1620.2 76372 3087.3
## + gender:parent_marital_status 3 125.2 74626 3087.7
## + parent_educ:transport_means 5 506.3 74245 3088.7
## + parent_marital_status:practice_sport 5 479.0 74272 3088.9
## + ethnic_group:practice_sport 8 1127.4 73624 3089.7
## + gender:parent_educ 5 368.0 74383 3089.8
## + parent_educ:lunch_type 5 259.4 74492 3090.6
## + parent_educ:test_prep 5 213.8 74538 3091.0
## + parent_educ:wkly_study_hours 10 1201.5 73550 3093.1
## + ethnic_group:wkly_study_hours 8 551.4 74200 3094.3
## - parent_marital_status:wkly_study_hours 6 3192.1 77943 3095.3
## - parent_marital_status:is_first_child 3 2981.5 77733 3099.7
## + ethnic_group:parent_educ 20 2531.3 72220 3102.3
##
## Step: AIC=3080.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 11.2 75534 3078.8
## - transport_means:wkly_study_hours 2 278.8 75802 3078.9
## - lunch_type:test_prep 1 35.1 75558 3079.0
## - practice_sport:transport_means 2 292.2 75815 3079.0
## - parent_marital_status:transport_means 3 569.2 76092 3079.2
## - gender:is_first_child 1 97.8 75621 3079.5
## - test_prep:practice_sport 2 392.1 75915 3079.8
## - gender:wkly_study_hours 2 415.8 75939 3080.0
## - is_first_child:transport_means 1 206.3 75729 3080.3
## - lunch_type:is_first_child 1 230.7 75754 3080.5
## - gender:practice_sport 2 488.1 76011 3080.5
## - test_prep:transport_means 1 243.1 75766 3080.6
## <none> 75523 3080.7
## - ethnic_group:is_first_child 4 1039.2 76562 3080.8
## - ethnic_group:parent_marital_status 11 2923.8 78447 3081.1
## - test_prep:wkly_study_hours 2 590.8 76114 3081.3
## - lunch_type:transport_means 1 353.3 75876 3081.5
## - parent_educ:practice_sport 10 2734.4 78257 3081.7
## - parent_educ:parent_marital_status 15 4073.2 79596 3081.7
## - practice_sport:wkly_study_hours 4 1215.7 76739 3082.1
## + ethnic_group:test_prep 4 771.6 74751 3082.7
## - ethnic_group:lunch_type 4 1286.4 76809 3082.7
## + gender:lunch_type 1 2.7 75520 3082.7
## + gender:transport_means 1 2.1 75521 3082.7
## + test_prep:is_first_child 1 1.5 75522 3082.7
## + test_prep:parent_marital_status 2 233.9 75289 3082.9
## + is_first_child:wkly_study_hours 2 112.4 75411 3083.8
## + parent_educ:is_first_child 5 859.8 74663 3084.0
## + practice_sport:is_first_child 2 84.3 75439 3084.1
## + lunch_type:parent_marital_status 3 334.5 75188 3084.1
## - lunch_type:wkly_study_hours 2 995.9 76519 3084.4
## - ethnic_group:transport_means 4 1599.8 77123 3085.1
## + gender:parent_marital_status 3 137.8 75385 3085.6
## - lunch_type:practice_sport 2 1217.2 76740 3086.2
## + gender:ethnic_group 4 290.9 75232 3086.4
## + parent_educ:transport_means 5 542.4 74981 3086.5
## + parent_marital_status:practice_sport 5 462.2 75061 3087.1
## + ethnic_group:practice_sport 8 1117.8 74405 3087.9
## + gender:parent_educ 5 330.2 75193 3088.1
## + parent_educ:lunch_type 5 277.0 75246 3088.6
## + parent_educ:test_prep 5 146.2 75377 3089.6
## + parent_educ:wkly_study_hours 10 1155.0 74368 3091.6
## - parent_marital_status:wkly_study_hours 6 3000.9 78524 3091.7
## + ethnic_group:wkly_study_hours 8 559.8 74963 3092.3
## - parent_marital_status:is_first_child 3 3061.0 78584 3098.2
## + ethnic_group:parent_educ 20 2514.4 73009 3100.7
##
## Step: AIC=3078.81
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 273.8 75808 3076.9
## - practice_sport:transport_means 2 292.1 75826 3077.1
## - lunch_type:test_prep 1 38.5 75573 3077.1
## - parent_marital_status:transport_means 3 575.3 76109 3077.3
## - gender:is_first_child 1 93.4 75627 3077.5
## - test_prep:practice_sport 2 389.8 75924 3077.8
## - gender:wkly_study_hours 2 432.6 75967 3078.2
## - is_first_child:transport_means 1 203.0 75737 3078.4
## - lunch_type:is_first_child 1 227.6 75762 3078.6
## - test_prep:transport_means 1 239.8 75774 3078.7
## - gender:practice_sport 2 500.9 76035 3078.7
## <none> 75534 3078.8
## - ethnic_group:is_first_child 4 1033.7 76568 3078.8
## - test_prep:wkly_study_hours 2 583.8 76118 3079.3
## - ethnic_group:parent_marital_status 11 2952.3 78486 3079.4
## - lunch_type:transport_means 1 358.4 75893 3079.6
## - parent_educ:parent_marital_status 15 4062.5 79597 3079.7
## - parent_educ:practice_sport 10 2755.3 78289 3079.9
## - practice_sport:wkly_study_hours 4 1211.3 76745 3080.2
## + gender:test_prep 1 11.2 75523 3080.7
## + gender:lunch_type 1 2.2 75532 3080.8
## - ethnic_group:lunch_type 4 1289.5 76824 3080.8
## + test_prep:is_first_child 1 1.4 75533 3080.8
## + gender:transport_means 1 1.2 75533 3080.8
## + ethnic_group:test_prep 4 751.4 74783 3080.9
## + test_prep:parent_marital_status 2 229.3 75305 3081.0
## + is_first_child:wkly_study_hours 2 113.7 75420 3081.9
## + parent_educ:is_first_child 5 858.1 74676 3082.1
## + practice_sport:is_first_child 2 86.3 75448 3082.1
## + lunch_type:parent_marital_status 3 338.3 75196 3082.2
## - lunch_type:wkly_study_hours 2 1005.4 76540 3082.6
## - ethnic_group:transport_means 4 1607.5 77142 3083.2
## + gender:parent_marital_status 3 142.5 75392 3083.7
## - lunch_type:practice_sport 2 1211.6 76746 3084.2
## + gender:ethnic_group 4 285.8 75248 3084.6
## + parent_educ:transport_means 5 532.2 75002 3084.6
## + parent_marital_status:practice_sport 5 465.2 75069 3085.2
## + ethnic_group:practice_sport 8 1103.3 74431 3086.1
## + gender:parent_educ 5 323.0 75211 3086.3
## + parent_educ:lunch_type 5 280.5 75254 3086.6
## + parent_educ:test_prep 5 151.5 75383 3087.6
## + parent_educ:wkly_study_hours 10 1155.9 74378 3089.7
## - parent_marital_status:wkly_study_hours 6 2990.8 78525 3089.7
## + ethnic_group:wkly_study_hours 8 568.8 74965 3090.3
## - parent_marital_status:is_first_child 3 3050.1 78584 3096.2
## + ethnic_group:parent_educ 20 2513.7 73020 3098.8
##
## Step: AIC=3076.94
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 37.1 75845 3075.2
## - parent_marital_status:transport_means 3 554.6 76363 3075.2
## - practice_sport:transport_means 2 311.7 76120 3075.4
## - gender:is_first_child 1 96.6 75905 3075.7
## - gender:wkly_study_hours 2 407.4 76215 3076.1
## - test_prep:practice_sport 2 424.4 76232 3076.2
## - is_first_child:transport_means 1 201.9 76010 3076.5
## - test_prep:transport_means 1 209.2 76017 3076.6
## - lunch_type:is_first_child 1 237.9 76046 3076.8
## - gender:practice_sport 2 498.4 76306 3076.8
## - ethnic_group:parent_marital_status 11 2879.7 78688 3076.9
## <none> 75808 3076.9
## - ethnic_group:is_first_child 4 1044.5 76852 3077.0
## - parent_educ:practice_sport 10 2625.6 78434 3077.0
## - test_prep:wkly_study_hours 2 530.9 76339 3077.1
## - parent_educ:parent_marital_status 15 4007.1 79815 3077.3
## - lunch_type:transport_means 1 332.9 76141 3077.5
## - practice_sport:wkly_study_hours 4 1234.7 77043 3078.5
## + transport_means:wkly_study_hours 2 273.8 75534 3078.8
## + gender:test_prep 1 6.2 75802 3078.9
## + gender:lunch_type 1 1.6 75806 3078.9
## + gender:transport_means 1 1.5 75806 3078.9
## - ethnic_group:lunch_type 4 1295.3 77103 3078.9
## + test_prep:is_first_child 1 0.3 75808 3078.9
## + ethnic_group:test_prep 4 760.2 75048 3079.0
## + test_prep:parent_marital_status 2 236.2 75572 3079.1
## + is_first_child:wkly_study_hours 2 128.6 75679 3079.9
## + lunch_type:parent_marital_status 3 366.5 75441 3080.1
## + parent_educ:is_first_child 5 860.6 74947 3080.2
## + practice_sport:is_first_child 2 86.9 75721 3080.3
## - lunch_type:wkly_study_hours 2 1028.6 76837 3080.9
## + gender:parent_marital_status 3 127.2 75681 3081.9
## - ethnic_group:transport_means 4 1734.7 77543 3082.3
## - lunch_type:practice_sport 2 1215.6 77024 3082.3
## + gender:ethnic_group 4 306.9 75501 3082.6
## + parent_educ:transport_means 5 551.3 75257 3082.6
## + parent_marital_status:practice_sport 5 473.7 75334 3083.2
## + ethnic_group:practice_sport 8 1130.4 74677 3084.1
## + gender:parent_educ 5 343.9 75464 3084.3
## + parent_educ:lunch_type 5 307.8 75500 3084.5
## + parent_educ:test_prep 5 146.0 75662 3085.8
## + parent_educ:wkly_study_hours 10 1197.1 74611 3087.6
## - parent_marital_status:wkly_study_hours 6 3056.3 78864 3088.3
## + ethnic_group:wkly_study_hours 8 470.4 75338 3089.3
## - parent_marital_status:is_first_child 3 2949.0 78757 3093.5
## + ethnic_group:parent_educ 20 2520.2 73288 3097.0
##
## Step: AIC=3075.23
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:transport_means 3 560.4 76405 3073.6
## - practice_sport:transport_means 2 322.3 76167 3073.7
## - gender:is_first_child 1 101.3 75946 3074.0
## - gender:wkly_study_hours 2 403.5 76249 3074.4
## - test_prep:practice_sport 2 429.6 76275 3074.6
## - is_first_child:transport_means 1 190.4 76035 3074.7
## - test_prep:transport_means 1 208.1 76053 3074.8
## - gender:practice_sport 2 491.6 76337 3075.0
## - ethnic_group:parent_marital_status 11 2862.4 78707 3075.1
## - lunch_type:is_first_child 1 242.6 76088 3075.1
## <none> 75845 3075.2
## - test_prep:wkly_study_hours 2 526.9 76372 3075.3
## - ethnic_group:is_first_child 4 1053.8 76899 3075.4
## - parent_educ:practice_sport 10 2648.9 78494 3075.5
## - lunch_type:transport_means 1 311.6 76157 3075.7
## - parent_educ:parent_marital_status 15 4021.2 79866 3075.7
## + lunch_type:test_prep 1 37.1 75808 3076.9
## - practice_sport:wkly_study_hours 4 1266.5 77111 3077.0
## + transport_means:wkly_study_hours 2 272.4 75573 3077.1
## + gender:test_prep 1 8.6 75836 3077.2
## + ethnic_group:test_prep 4 772.6 75072 3077.2
## + gender:lunch_type 1 2.6 75842 3077.2
## + gender:transport_means 1 1.9 75843 3077.2
## + test_prep:is_first_child 1 0.4 75845 3077.2
## + test_prep:parent_marital_status 2 236.9 75608 3077.4
## - ethnic_group:lunch_type 4 1340.5 77186 3077.6
## + is_first_child:wkly_study_hours 2 137.2 75708 3078.2
## + lunch_type:parent_marital_status 3 366.8 75478 3078.4
## + practice_sport:is_first_child 2 91.2 75754 3078.5
## + parent_educ:is_first_child 5 842.0 75003 3078.7
## - lunch_type:wkly_study_hours 2 1005.4 76850 3079.0
## + gender:parent_marital_status 3 121.2 75724 3080.3
## - lunch_type:practice_sport 2 1201.8 77047 3080.5
## - ethnic_group:transport_means 4 1735.4 77580 3080.6
## + gender:ethnic_group 4 317.8 75527 3080.8
## + parent_educ:transport_means 5 567.5 75278 3080.8
## + parent_marital_status:practice_sport 5 467.7 75377 3081.6
## + ethnic_group:practice_sport 8 1157.3 74688 3082.2
## + gender:parent_educ 5 355.3 75490 3082.5
## + parent_educ:lunch_type 5 301.9 75543 3082.9
## + parent_educ:test_prep 5 144.0 75701 3084.1
## + parent_educ:wkly_study_hours 10 1215.6 74629 3085.7
## - parent_marital_status:wkly_study_hours 6 3086.6 78932 3086.8
## + ethnic_group:wkly_study_hours 8 482.4 75363 3087.5
## - parent_marital_status:is_first_child 3 2971.6 78817 3091.9
## + ethnic_group:parent_educ 20 2528.3 73317 3095.2
##
## Step: AIC=3073.57
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 289.2 76695 3071.8
## - gender:is_first_child 1 104.0 76509 3072.4
## - parent_educ:parent_marital_status 15 3830.4 80236 3072.4
## - gender:wkly_study_hours 2 397.3 76803 3072.6
## - test_prep:practice_sport 2 408.6 76814 3072.7
## - ethnic_group:parent_marital_status 11 2815.5 79221 3072.9
## - gender:practice_sport 2 469.1 76875 3073.2
## - test_prep:transport_means 1 227.5 76633 3073.3
## - lunch_type:is_first_child 1 235.1 76640 3073.4
## - test_prep:wkly_study_hours 2 513.5 76919 3073.5
## <none> 76405 3073.6
## - ethnic_group:is_first_child 4 1050.0 77455 3073.6
## - is_first_child:transport_means 1 266.4 76672 3073.6
## - lunch_type:transport_means 1 334.7 76740 3074.2
## - parent_educ:practice_sport 10 2736.7 79142 3074.3
## - practice_sport:wkly_study_hours 4 1246.9 77652 3075.1
## + test_prep:parent_marital_status 2 308.7 76097 3075.2
## + parent_marital_status:transport_means 3 560.4 75845 3075.2
## + lunch_type:test_prep 1 42.8 76363 3075.2
## + gender:test_prep 1 14.8 76391 3075.5
## + gender:lunch_type 1 1.2 76404 3075.6
## + gender:transport_means 1 1.0 76404 3075.6
## + test_prep:is_first_child 1 0.1 76405 3075.6
## + transport_means:wkly_study_hours 2 249.8 76156 3075.6
## - ethnic_group:lunch_type 4 1321.6 77727 3075.7
## + ethnic_group:test_prep 4 702.7 75703 3076.1
## + lunch_type:parent_marital_status 3 361.0 76044 3076.8
## + is_first_child:wkly_study_hours 2 83.7 76322 3076.9
## + practice_sport:is_first_child 2 61.6 76344 3077.1
## - lunch_type:wkly_study_hours 2 1054.0 77459 3077.7
## - ethnic_group:transport_means 4 1591.6 77997 3077.7
## + parent_educ:is_first_child 5 718.4 75687 3078.0
## + gender:parent_marital_status 3 187.7 76218 3078.1
## + gender:ethnic_group 4 335.7 76070 3079.0
## - lunch_type:practice_sport 2 1274.9 77680 3079.3
## + parent_educ:transport_means 5 466.6 75939 3080.0
## + parent_marital_status:practice_sport 5 458.2 75947 3080.0
## + ethnic_group:practice_sport 8 1209.6 75196 3080.2
## + gender:parent_educ 5 401.7 76004 3080.5
## + parent_educ:lunch_type 5 307.1 76098 3081.2
## + parent_educ:test_prep 5 119.6 76286 3082.7
## - parent_marital_status:wkly_study_hours 6 2935.7 79341 3083.8
## + parent_educ:wkly_study_hours 10 1232.7 75173 3084.0
## + ethnic_group:wkly_study_hours 8 494.3 75911 3085.8
## - parent_marital_status:is_first_child 3 3121.7 79527 3091.2
## + ethnic_group:parent_educ 20 2414.4 73991 3094.6
##
## Step: AIC=3071.8
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - parent_educ:parent_marital_status 15 3742.3 80437 3069.9
## - ethnic_group:parent_marital_status 11 2688.4 79383 3070.1
## - test_prep:practice_sport 2 378.6 77073 3070.7
## - gender:is_first_child 1 134.4 76829 3070.8
## - gender:wkly_study_hours 2 415.0 77109 3071.0
## - gender:practice_sport 2 415.5 77110 3071.0
## - test_prep:transport_means 1 209.1 76904 3071.4
## - lunch_type:is_first_child 1 249.4 76944 3071.7
## - ethnic_group:is_first_child 4 1038.9 77733 3071.7
## - test_prep:wkly_study_hours 2 514.3 77209 3071.8
## <none> 76695 3071.8
## - parent_educ:practice_sport 10 2659.6 79354 3071.9
## - is_first_child:transport_means 1 324.1 77019 3072.3
## - lunch_type:transport_means 1 352.1 77047 3072.5
## - practice_sport:wkly_study_hours 4 1213.3 77908 3073.1
## + test_prep:parent_marital_status 2 318.9 76376 3073.3
## + lunch_type:test_prep 1 53.6 76641 3073.4
## + practice_sport:transport_means 2 289.2 76405 3073.6
## - ethnic_group:lunch_type 4 1283.1 77978 3073.6
## + gender:test_prep 1 15.0 76680 3073.7
## + transport_means:wkly_study_hours 2 270.1 76424 3073.7
## + parent_marital_status:transport_means 3 527.2 76167 3073.7
## + gender:lunch_type 1 2.2 76692 3073.8
## + gender:transport_means 1 1.1 76693 3073.8
## + test_prep:is_first_child 1 0.2 76694 3073.8
## + ethnic_group:test_prep 4 713.2 75981 3074.3
## + lunch_type:parent_marital_status 3 359.8 76335 3075.0
## + is_first_child:wkly_study_hours 2 90.4 76604 3075.1
## + practice_sport:is_first_child 2 60.5 76634 3075.3
## - lunch_type:wkly_study_hours 2 1032.8 77727 3075.7
## - ethnic_group:transport_means 4 1618.0 78313 3076.1
## + parent_educ:is_first_child 5 721.0 75974 3076.2
## + gender:parent_marital_status 3 164.7 76530 3076.5
## + gender:ethnic_group 4 328.7 76366 3077.3
## - lunch_type:practice_sport 2 1255.8 77950 3077.4
## + parent_marital_status:practice_sport 5 444.6 76250 3078.4
## + ethnic_group:practice_sport 8 1203.1 75491 3078.5
## + parent_educ:transport_means 5 422.0 76273 3078.6
## + gender:parent_educ 5 396.2 76298 3078.8
## + parent_educ:lunch_type 5 370.5 76324 3078.9
## + parent_educ:test_prep 5 141.0 76554 3080.7
## - parent_marital_status:wkly_study_hours 6 2936.1 79631 3082.0
## + parent_educ:wkly_study_hours 10 1143.1 75551 3082.9
## + ethnic_group:wkly_study_hours 8 499.7 76195 3083.9
## - parent_marital_status:is_first_child 3 3103.2 79798 3089.2
## + ethnic_group:parent_educ 20 2362.4 74332 3093.3
##
## Step: AIC=3069.91
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 252.6 80689 3067.8
## - ethnic_group:is_first_child 4 845.9 81283 3068.1
## - gender:wkly_study_hours 2 337.8 80775 3068.4
## - ethnic_group:lunch_type 4 964.9 81402 3068.9
## - gender:is_first_child 1 152.4 80589 3069.0
## - gender:practice_sport 2 443.1 80880 3069.2
## - test_prep:wkly_study_hours 2 487.4 80924 3069.5
## <none> 80437 3069.9
## - is_first_child:transport_means 1 291.8 80729 3070.1
## - ethnic_group:parent_marital_status 11 3119.9 83557 3070.4
## - test_prep:transport_means 1 338.9 80776 3070.4
## - practice_sport:wkly_study_hours 4 1165.6 81602 3070.4
## - lunch_type:is_first_child 1 392.2 80829 3070.8
## - lunch_type:transport_means 1 419.3 80856 3071.0
## - parent_educ:practice_sport 10 2963.0 83400 3071.2
## + lunch_type:test_prep 1 63.2 80374 3071.4
## + parent_educ:parent_marital_status 15 3742.3 76695 3071.8
## + gender:transport_means 1 14.0 80423 3071.8
## + gender:lunch_type 1 1.8 80435 3071.9
## + gender:test_prep 1 1.5 80435 3071.9
## + test_prep:is_first_child 1 0.2 80437 3071.9
## + transport_means:wkly_study_hours 2 233.9 80203 3072.2
## + practice_sport:transport_means 2 201.1 80236 3072.4
## + is_first_child:wkly_study_hours 2 171.6 80265 3072.7
## + ethnic_group:test_prep 4 689.7 79747 3072.8
## + parent_marital_status:transport_means 3 369.7 80067 3073.2
## + lunch_type:parent_marital_status 3 335.5 80101 3073.4
## + practice_sport:is_first_child 2 26.1 80411 3073.7
## + test_prep:parent_marital_status 3 293.2 80144 3073.8
## + parent_educ:is_first_child 5 730.0 79707 3074.5
## - ethnic_group:transport_means 4 1749.2 82186 3074.6
## + gender:ethnic_group 4 429.6 80007 3074.8
## - lunch_type:practice_sport 2 1226.7 81664 3074.8
## + gender:parent_educ 5 654.3 79783 3075.1
## - lunch_type:wkly_study_hours 2 1303.3 81740 3075.4
## + parent_marital_status:practice_sport 6 872.2 79565 3075.5
## + gender:parent_marital_status 3 19.2 80418 3075.8
## + parent_educ:transport_means 5 433.9 80003 3076.7
## + parent_educ:lunch_type 5 383.9 80053 3077.1
## + ethnic_group:practice_sport 8 1150.9 79286 3077.4
## - parent_marital_status:wkly_study_hours 6 2787.1 83224 3078.0
## + parent_educ:wkly_study_hours 10 1534.7 78902 3078.6
## + parent_educ:test_prep 5 161.9 80275 3078.7
## + ethnic_group:wkly_study_hours 8 363.2 80074 3083.2
## - parent_marital_status:is_first_child 3 3025.4 83462 3085.7
## + ethnic_group:parent_educ 20 2639.7 77797 3090.2
##
## Step: AIC=3067.76
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:wkly_study_hours 2 317.4 81007 3066.1
## - ethnic_group:is_first_child 4 876.0 81565 3066.1
## - gender:is_first_child 1 149.2 80839 3066.8
## - ethnic_group:lunch_type 4 1028.7 81718 3067.2
## - test_prep:wkly_study_hours 2 478.9 81168 3067.2
## - gender:practice_sport 2 482.9 81172 3067.3
## <none> 80689 3067.8
## - is_first_child:transport_means 1 301.4 80991 3068.0
## - ethnic_group:parent_marital_status 11 3122.9 83812 3068.2
## - test_prep:transport_means 1 362.3 81052 3068.4
## - practice_sport:wkly_study_hours 4 1204.8 81894 3068.5
## - lunch_type:transport_means 1 401.7 81091 3068.7
## - lunch_type:is_first_child 1 414.9 81104 3068.8
## - parent_educ:practice_sport 10 2989.8 83679 3069.2
## + lunch_type:test_prep 1 68.9 80620 3069.3
## + gender:transport_means 1 16.0 80673 3069.6
## + gender:lunch_type 1 3.0 80686 3069.7
## + gender:test_prep 1 0.9 80689 3069.8
## + test_prep:is_first_child 1 0.5 80689 3069.8
## + test_prep:practice_sport 2 252.6 80437 3069.9
## + transport_means:wkly_study_hours 2 250.9 80439 3069.9
## + practice_sport:transport_means 2 179.0 80510 3070.4
## + parent_educ:parent_marital_status 15 3616.3 77073 3070.7
## + is_first_child:wkly_study_hours 2 142.8 80547 3070.7
## + ethnic_group:test_prep 4 679.6 80010 3070.8
## + parent_marital_status:transport_means 3 354.1 80335 3071.2
## + lunch_type:parent_marital_status 3 344.3 80345 3071.2
## + test_prep:parent_marital_status 3 342.7 80347 3071.2
## + practice_sport:is_first_child 2 29.2 80660 3071.6
## + parent_educ:is_first_child 5 816.0 79873 3071.8
## - ethnic_group:transport_means 4 1694.6 82384 3072.0
## + gender:parent_educ 5 703.6 79986 3072.6
## + gender:ethnic_group 4 422.9 80266 3072.7
## + parent_marital_status:practice_sport 6 896.9 79792 3073.2
## - lunch_type:practice_sport 2 1303.1 81992 3073.2
## + gender:parent_marital_status 3 35.1 80654 3073.5
## - lunch_type:wkly_study_hours 2 1383.7 82073 3073.8
## + parent_educ:transport_means 5 451.8 80238 3074.4
## + parent_educ:lunch_type 5 429.1 80260 3074.6
## - parent_marital_status:wkly_study_hours 6 2769.9 83459 3075.7
## + ethnic_group:practice_sport 8 1090.2 79599 3075.7
## + parent_educ:wkly_study_hours 10 1608.6 79081 3075.9
## + parent_educ:test_prep 5 143.5 80546 3076.7
## + ethnic_group:wkly_study_hours 8 358.2 80331 3081.1
## - parent_marital_status:is_first_child 3 3049.0 83738 3083.6
## + ethnic_group:parent_educ 20 2713.0 77976 3087.6
##
## Step: AIC=3066.08
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:practice_sport + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - ethnic_group:is_first_child 4 824.9 81832 3064.1
## - gender:is_first_child 1 157.3 81164 3065.2
## - test_prep:wkly_study_hours 2 469.7 81477 3065.5
## - ethnic_group:lunch_type 4 1034.1 82041 3065.6
## - gender:practice_sport 2 527.0 81534 3065.9
## - is_first_child:transport_means 1 270.8 81278 3066.1
## <none> 81007 3066.1
## - ethnic_group:parent_marital_status 11 3080.5 84087 3066.1
## - practice_sport:wkly_study_hours 4 1177.4 82184 3066.6
## - test_prep:transport_means 1 371.6 81378 3066.8
## - lunch_type:is_first_child 1 398.6 81405 3067.0
## - lunch_type:transport_means 1 411.4 81418 3067.1
## + lunch_type:test_prep 1 65.7 80941 3067.6
## + gender:wkly_study_hours 2 317.4 80689 3067.8
## - parent_educ:practice_sport 10 3056.9 84064 3067.9
## + gender:transport_means 1 14.9 80992 3068.0
## + gender:test_prep 1 6.9 81000 3068.0
## + test_prep:is_first_child 1 4.0 81003 3068.1
## + gender:lunch_type 1 1.5 81005 3068.1
## + test_prep:practice_sport 2 232.2 80775 3068.4
## + transport_means:wkly_study_hours 2 227.6 80779 3068.4
## + practice_sport:transport_means 2 188.6 80818 3068.7
## + is_first_child:wkly_study_hours 2 133.4 80873 3069.1
## + ethnic_group:test_prep 4 673.4 80333 3069.2
## + test_prep:parent_marital_status 3 361.5 80645 3069.4
## + parent_marital_status:transport_means 3 350.5 80656 3069.5
## + parent_educ:parent_marital_status 15 3542.0 77465 3069.7
## + practice_sport:is_first_child 2 23.4 80983 3069.9
## + lunch_type:parent_marital_status 3 291.6 80715 3069.9
## - ethnic_group:transport_means 4 1664.0 82671 3070.1
## + parent_educ:is_first_child 5 765.7 80241 3070.5
## + gender:ethnic_group 4 458.3 80549 3070.7
## + gender:parent_educ 5 716.2 80291 3070.8
## - lunch_type:wkly_study_hours 2 1298.7 82306 3071.5
## + parent_marital_status:practice_sport 6 903.1 80104 3071.5
## - lunch_type:practice_sport 2 1320.2 82327 3071.6
## + gender:parent_marital_status 3 51.8 80955 3071.7
## + parent_educ:transport_means 5 408.3 80598 3073.1
## + parent_educ:wkly_study_hours 10 1753.4 79253 3073.2
## + parent_educ:lunch_type 5 387.2 80620 3073.2
## + ethnic_group:practice_sport 8 1147.0 79860 3073.7
## + parent_educ:test_prep 5 166.8 80840 3074.9
## - parent_marital_status:wkly_study_hours 6 3058.9 84066 3075.9
## + ethnic_group:wkly_study_hours 8 326.3 80680 3079.7
## - parent_marital_status:is_first_child 3 2917.4 83924 3080.9
## + ethnic_group:parent_educ 20 2718.5 78288 3085.9
##
## Step: AIC=3064.06
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - ethnic_group:lunch_type 4 852.1 82684 3062.2
## - ethnic_group:parent_marital_status 11 2845.2 84677 3062.2
## - test_prep:wkly_study_hours 2 337.2 82169 3062.5
## - gender:is_first_child 1 92.9 81925 3062.7
## - is_first_child:transport_means 1 144.4 81976 3063.1
## - gender:practice_sport 2 513.8 82346 3063.8
## <none> 81832 3064.1
## - test_prep:transport_means 1 331.1 82163 3064.4
## - lunch_type:transport_means 1 353.6 82185 3064.6
## - practice_sport:wkly_study_hours 4 1203.5 83035 3064.7
## + lunch_type:test_prep 1 70.7 81761 3065.6
## - parent_educ:practice_sport 10 3037.2 84869 3065.6
## - lunch_type:is_first_child 1 516.8 82349 3065.8
## + test_prep:is_first_child 1 12.1 81820 3066.0
## + gender:transport_means 1 11.6 81820 3066.0
## + gender:test_prep 1 3.5 81828 3066.0
## + gender:lunch_type 1 1.2 81830 3066.1
## + ethnic_group:is_first_child 4 824.9 81007 3066.1
## + test_prep:practice_sport 2 268.1 81564 3066.1
## + gender:wkly_study_hours 2 266.2 81565 3066.1
## + transport_means:wkly_study_hours 2 249.9 81582 3066.2
## + is_first_child:wkly_study_hours 2 194.0 81638 3066.7
## + practice_sport:transport_means 2 186.5 81645 3066.7
## + ethnic_group:test_prep 4 728.6 81103 3066.8
## + test_prep:parent_marital_status 3 433.6 81398 3066.9
## + parent_marital_status:transport_means 3 351.9 81480 3067.5
## + practice_sport:is_first_child 2 25.3 81806 3067.9
## + lunch_type:parent_marital_status 3 240.0 81592 3068.3
## + parent_educ:is_first_child 5 786.2 81046 3068.4
## + gender:ethnic_group 4 454.0 81378 3068.8
## - lunch_type:wkly_study_hours 2 1224.7 83056 3068.8
## + gender:parent_educ 5 703.5 81128 3069.0
## + parent_educ:parent_marital_status 15 3382.9 78449 3069.2
## - lunch_type:practice_sport 2 1335.5 83167 3069.6
## + parent_marital_status:practice_sport 6 882.2 80950 3069.7
## - ethnic_group:transport_means 4 1911.7 83743 3069.7
## + gender:parent_marital_status 3 35.0 81797 3069.8
## + parent_educ:wkly_study_hours 10 1830.4 80001 3070.7
## + parent_educ:transport_means 5 445.2 81387 3070.8
## + parent_educ:lunch_type 5 377.7 81454 3071.3
## + ethnic_group:practice_sport 8 1069.7 80762 3072.3
## + parent_educ:test_prep 5 160.9 81671 3072.9
## - parent_marital_status:wkly_study_hours 6 2994.3 84826 3073.3
## - parent_marital_status:is_first_child 3 2566.9 84399 3076.3
## + ethnic_group:wkly_study_hours 8 354.1 81478 3077.5
## + ethnic_group:parent_educ 20 2784.5 79047 3083.6
##
## Step: AIC=3062.17
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + ethnic_group:parent_marital_status +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_marital_status 11 2792.28 85476 3059.8
## - test_prep:wkly_study_hours 2 332.30 83016 3060.5
## - gender:is_first_child 1 84.77 82769 3060.8
## - is_first_child:transport_means 1 122.86 82807 3061.0
## - gender:practice_sport 2 436.01 83120 3061.3
## - practice_sport:wkly_study_hours 4 1064.27 83748 3061.7
## <none> 82684 3062.2
## - test_prep:transport_means 1 367.25 83051 3062.8
## - lunch_type:transport_means 1 416.94 83101 3063.1
## + lunch_type:test_prep 1 106.82 82577 3063.4
## - lunch_type:is_first_child 1 457.20 83141 3063.4
## + test_prep:practice_sport 2 327.08 82357 3063.8
## - parent_educ:practice_sport 10 3101.14 85785 3063.9
## + ethnic_group:lunch_type 4 852.14 81832 3064.1
## + gender:transport_means 1 14.86 82669 3064.1
## + test_prep:is_first_child 1 5.78 82678 3064.1
## + gender:lunch_type 1 5.44 82678 3064.1
## + gender:test_prep 1 4.70 82679 3064.1
## + gender:wkly_study_hours 2 272.64 82411 3064.2
## + transport_means:wkly_study_hours 2 254.90 82429 3064.3
## + is_first_child:wkly_study_hours 2 193.27 82491 3064.8
## + test_prep:parent_marital_status 3 449.82 82234 3064.9
## + practice_sport:transport_means 2 155.79 82528 3065.1
## + ethnic_group:is_first_child 4 642.90 82041 3065.6
## + parent_marital_status:transport_means 3 349.67 82334 3065.7
## + practice_sport:is_first_child 2 33.45 82650 3065.9
## + ethnic_group:test_prep 4 566.41 82117 3066.1
## + parent_educ:is_first_child 5 839.05 81845 3066.2
## - lunch_type:wkly_study_hours 2 1133.23 83817 3066.2
## + lunch_type:parent_marital_status 3 269.52 82414 3066.2
## + gender:ethnic_group 4 456.00 82228 3066.9
## - ethnic_group:transport_means 4 1846.35 84530 3067.2
## + parent_marital_status:practice_sport 6 954.98 81729 3067.3
## + gender:parent_educ 5 616.92 82067 3067.8
## + gender:parent_marital_status 3 37.83 82646 3067.9
## + parent_educ:transport_means 5 525.02 82159 3068.4
## - lunch_type:practice_sport 2 1543.54 84227 3069.1
## + parent_educ:parent_marital_status 15 3130.53 79553 3069.4
## + ethnic_group:practice_sport 8 1213.72 81470 3069.4
## + parent_educ:lunch_type 5 340.93 82343 3069.7
## + parent_educ:test_prep 5 161.91 82522 3071.0
## + parent_educ:wkly_study_hours 10 1527.60 81156 3071.2
## - parent_marital_status:wkly_study_hours 6 3050.50 85734 3071.5
## - parent_marital_status:is_first_child 3 2646.16 85330 3074.8
## + ethnic_group:wkly_study_hours 8 326.65 82357 3075.8
## + ethnic_group:parent_educ 20 2852.94 79831 3081.4
##
## Step: AIC=3059.76
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 99.6 85576 3058.4
## - practice_sport:wkly_study_hours 4 1008.6 86485 3058.7
## - test_prep:wkly_study_hours 2 479.0 85955 3059.1
## - is_first_child:transport_means 1 198.2 85674 3059.1
## - gender:practice_sport 2 564.4 86041 3059.7
## <none> 85476 3059.8
## - lunch_type:is_first_child 1 308.3 85784 3059.9
## - parent_educ:practice_sport 10 2978.9 88455 3060.0
## - test_prep:transport_means 1 364.2 85840 3060.3
## - lunch_type:transport_means 1 417.7 85894 3060.6
## + test_prep:practice_sport 2 328.5 85148 3061.5
## + lunch_type:test_prep 1 32.5 85444 3061.5
## + gender:test_prep 1 14.8 85461 3061.7
## + test_prep:is_first_child 1 1.7 85474 3061.8
## + gender:lunch_type 1 0.3 85476 3061.8
## + gender:transport_means 1 0.0 85476 3061.8
## + transport_means:wkly_study_hours 2 244.4 85232 3062.1
## + gender:wkly_study_hours 2 237.4 85239 3062.1
## + ethnic_group:parent_marital_status 11 2792.3 82684 3062.2
## + ethnic_group:lunch_type 4 799.3 84677 3062.2
## + practice_sport:transport_means 2 103.1 85373 3063.1
## + parent_marital_status:transport_means 3 372.4 85104 3063.2
## - lunch_type:wkly_study_hours 2 1083.0 86559 3063.2
## + is_first_child:wkly_study_hours 2 80.1 85396 3063.2
## + lunch_type:parent_marital_status 3 364.8 85111 3063.2
## + test_prep:parent_marital_status 3 353.5 85123 3063.3
## + parent_educ:parent_marital_status 15 3706.0 81770 3063.6
## + practice_sport:is_first_child 2 15.9 85460 3063.7
## - ethnic_group:transport_means 4 1765.3 87241 3063.8
## + ethnic_group:test_prep 4 491.6 84985 3064.4
## + parent_marital_status:practice_sport 6 1039.9 84436 3064.5
## + parent_educ:is_first_child 5 744.1 84732 3064.6
## + gender:parent_marital_status 3 152.7 85323 3064.7
## + ethnic_group:is_first_child 4 412.6 85064 3064.9
## + gender:ethnic_group 4 376.8 85099 3065.2
## - parent_marital_status:wkly_study_hours 6 2624.6 88101 3065.6
## + parent_educ:transport_means 5 566.9 84909 3065.8
## + parent_educ:wkly_study_hours 10 1851.9 83624 3066.8
## + gender:parent_educ 5 421.5 85055 3066.8
## + ethnic_group:practice_sport 8 1241.8 84234 3067.1
## - lunch_type:practice_sport 2 1699.0 87175 3067.4
## + parent_educ:lunch_type 5 306.9 85169 3067.6
## - parent_marital_status:is_first_child 3 2204.5 87681 3068.8
## + parent_educ:test_prep 5 128.8 85347 3068.9
## + ethnic_group:wkly_study_hours 8 315.5 85161 3073.6
## + ethnic_group:parent_educ 20 2736.0 82740 3080.6
##
## Step: AIC=3058.45
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - test_prep:wkly_study_hours 2 466.5 86042 3057.7
## - practice_sport:wkly_study_hours 4 1055.8 86632 3057.7
## - is_first_child:transport_means 1 187.3 85763 3057.7
## - lunch_type:is_first_child 1 290.5 85866 3058.4
## <none> 85576 3058.4
## - gender:practice_sport 2 587.3 86163 3058.5
## - test_prep:transport_means 1 362.2 85938 3058.9
## - parent_educ:practice_sport 10 3073.1 88649 3059.3
## - lunch_type:transport_means 1 454.6 86030 3059.6
## + gender:is_first_child 1 99.6 85476 3059.8
## + lunch_type:test_prep 1 36.7 85539 3060.2
## + test_prep:practice_sport 2 321.6 85254 3060.2
## + gender:test_prep 1 10.1 85566 3060.4
## + test_prep:is_first_child 1 3.9 85572 3060.4
## + gender:lunch_type 1 0.3 85575 3060.4
## + gender:transport_means 1 0.0 85576 3060.4
## + ethnic_group:parent_marital_status 11 2807.1 82769 3060.8
## + gender:wkly_study_hours 2 239.8 85336 3060.8
## + transport_means:wkly_study_hours 2 235.6 85340 3060.8
## + ethnic_group:lunch_type 4 790.3 84785 3061.0
## + practice_sport:transport_means 2 119.8 85456 3061.6
## - lunch_type:wkly_study_hours 2 1069.3 86645 3061.8
## + is_first_child:wkly_study_hours 2 93.1 85483 3061.8
## + parent_marital_status:transport_means 3 378.6 85197 3061.8
## + lunch_type:parent_marital_status 3 373.1 85203 3061.9
## + test_prep:parent_marital_status 3 366.2 85210 3061.9
## + practice_sport:is_first_child 2 17.0 85559 3062.3
## + parent_educ:parent_marital_status 15 3677.7 81898 3062.5
## - ethnic_group:transport_means 4 1832.9 87409 3062.9
## + ethnic_group:test_prep 4 469.5 85106 3063.2
## + parent_educ:is_first_child 5 746.7 84829 3063.3
## + gender:parent_marital_status 3 164.8 85411 3063.3
## + parent_marital_status:practice_sport 6 1021.0 84555 3063.4
## + gender:ethnic_group 4 396.7 85179 3063.7
## - parent_marital_status:wkly_study_hours 6 2559.8 88136 3063.8
## + ethnic_group:is_first_child 4 373.2 85203 3063.9
## + parent_educ:transport_means 5 547.7 85028 3064.7
## + parent_educ:wkly_study_hours 10 1883.7 83692 3065.3
## + gender:parent_educ 5 423.0 85153 3065.5
## + parent_educ:lunch_type 5 345.4 85230 3066.1
## + ethnic_group:practice_sport 8 1193.1 84383 3066.2
## - lunch_type:practice_sport 2 1747.0 87323 3066.4
## - parent_marital_status:is_first_child 3 2145.8 87722 3067.1
## + parent_educ:test_prep 5 132.8 85443 3067.5
## + ethnic_group:wkly_study_hours 8 314.1 85262 3072.3
## + ethnic_group:parent_educ 20 2622.3 82953 3080.1
##
## Step: AIC=3057.66
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - is_first_child:transport_means 1 180.8 86223 3056.9
## - practice_sport:wkly_study_hours 4 1089.4 87132 3057.1
## - parent_educ:practice_sport 10 2918.5 88961 3057.3
## - lunch_type:is_first_child 1 245.9 86288 3057.3
## - gender:practice_sport 2 569.1 86611 3057.6
## <none> 86042 3057.7
## - test_prep:transport_means 1 322.8 86365 3057.9
## - lunch_type:transport_means 1 347.8 86390 3058.0
## + test_prep:wkly_study_hours 2 466.5 85576 3058.4
## + ethnic_group:parent_marital_status 11 2953.0 83089 3059.1
## + gender:is_first_child 1 87.1 85955 3059.1
## + lunch_type:test_prep 1 28.5 86014 3059.5
## + test_prep:practice_sport 2 315.9 85726 3059.5
## + gender:test_prep 1 3.7 86039 3059.6
## + test_prep:is_first_child 1 2.4 86040 3059.6
## + gender:lunch_type 1 0.5 86042 3059.7
## + gender:transport_means 1 0.1 86042 3059.7
## + gender:wkly_study_hours 2 231.2 85811 3060.1
## + transport_means:wkly_study_hours 2 203.4 85839 3060.3
## + ethnic_group:lunch_type 4 765.9 85276 3060.4
## + practice_sport:transport_means 2 121.1 85921 3060.8
## + is_first_child:wkly_study_hours 2 80.3 85962 3061.1
## + parent_marital_status:transport_means 3 367.4 85675 3061.1
## + test_prep:parent_marital_status 3 353.3 85689 3061.2
## + lunch_type:parent_marital_status 3 351.9 85690 3061.2
## - lunch_type:wkly_study_hours 2 1130.2 87172 3061.4
## + practice_sport:is_first_child 2 22.1 86020 3061.5
## - ethnic_group:transport_means 4 1762.4 87805 3061.6
## + ethnic_group:test_prep 4 563.0 85479 3061.8
## + parent_educ:parent_marital_status 15 3637.1 82405 3062.2
## + parent_educ:is_first_child 5 782.3 85260 3062.3
## + parent_marital_status:practice_sport 6 1062.0 84980 3062.3
## + gender:parent_marital_status 3 132.6 85910 3062.8
## + gender:ethnic_group 4 414.5 85628 3062.8
## - parent_marital_status:wkly_study_hours 6 2558.9 88601 3062.9
## + parent_educ:wkly_study_hours 10 2045.6 83997 3063.5
## + parent_educ:transport_means 5 565.0 85477 3063.8
## + ethnic_group:is_first_child 4 274.4 85768 3063.8
## + gender:parent_educ 5 469.8 85572 3064.4
## - lunch_type:practice_sport 2 1596.3 87639 3064.5
## + parent_educ:lunch_type 5 353.9 85688 3065.2
## + ethnic_group:practice_sport 8 1091.5 84951 3066.1
## - parent_marital_status:is_first_child 3 2170.7 88213 3066.4
## + parent_educ:test_prep 5 135.1 85907 3066.7
## + ethnic_group:wkly_study_hours 8 351.6 85691 3071.2
## + ethnic_group:parent_educ 20 2649.4 83393 3079.2
##
## Step: AIC=3056.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:practice_sport 10 2832.5 89055 3056.0
## - practice_sport:wkly_study_hours 4 1063.9 87287 3056.1
## - lunch_type:is_first_child 1 244.7 86468 3056.6
## <none> 86223 3056.9
## - gender:practice_sport 2 601.5 86825 3057.0
## - lunch_type:transport_means 1 345.2 86568 3057.2
## - test_prep:transport_means 1 351.2 86574 3057.3
## + is_first_child:transport_means 1 180.8 86042 3057.7
## + test_prep:wkly_study_hours 2 459.9 85763 3057.7
## + ethnic_group:parent_marital_status 11 3020.0 83203 3057.9
## + gender:is_first_child 1 77.2 86146 3058.4
## + test_prep:practice_sport 2 317.0 85906 3058.7
## + lunch_type:test_prep 1 18.6 86204 3058.8
## + test_prep:is_first_child 1 4.4 86219 3058.9
## + gender:test_prep 1 2.5 86221 3058.9
## + gender:transport_means 1 1.6 86221 3058.9
## + gender:lunch_type 1 0.0 86223 3058.9
## + gender:wkly_study_hours 2 214.7 86008 3059.4
## + transport_means:wkly_study_hours 2 201.8 86021 3059.5
## + ethnic_group:lunch_type 4 760.6 85462 3059.7
## + practice_sport:transport_means 2 138.2 86085 3059.9
## + parent_marital_status:transport_means 3 425.2 85798 3060.0
## + is_first_child:wkly_study_hours 2 66.5 86156 3060.4
## + test_prep:parent_marital_status 3 354.6 85868 3060.5
## + lunch_type:parent_marital_status 3 348.9 85874 3060.5
## + practice_sport:is_first_child 2 15.4 86208 3060.8
## - ethnic_group:transport_means 4 1773.5 87996 3060.9
## + ethnic_group:test_prep 4 562.5 85660 3061.0
## - lunch_type:wkly_study_hours 2 1200.3 87423 3061.1
## + parent_educ:is_first_child 5 810.7 85412 3061.3
## + parent_educ:parent_marital_status 15 3644.1 82579 3061.4
## + parent_marital_status:practice_sport 6 1060.8 85162 3061.6
## + gender:ethnic_group 4 447.2 85776 3061.8
## - parent_marital_status:wkly_study_hours 6 2529.8 88753 3062.0
## + gender:parent_marital_status 3 115.9 86107 3062.1
## + parent_educ:wkly_study_hours 10 2054.9 84168 3062.7
## + parent_educ:transport_means 5 527.1 85696 3063.3
## - lunch_type:practice_sport 2 1567.4 87790 3063.5
## + ethnic_group:is_first_child 4 198.1 86025 3063.5
## + gender:parent_educ 5 456.3 85767 3063.8
## + parent_educ:lunch_type 5 338.7 85884 3064.6
## + ethnic_group:practice_sport 8 1146.4 85077 3065.0
## - parent_marital_status:is_first_child 3 2120.8 88344 3065.2
## + parent_educ:test_prep 5 168.1 86055 3065.7
## + ethnic_group:wkly_study_hours 8 368.5 85854 3070.4
## + ethnic_group:parent_educ 20 2575.7 83647 3079.0
##
## Step: AIC=3055.97
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 914.5 89970 3054.0
## - gender:practice_sport 2 409.2 89465 3054.7
## - lunch_type:is_first_child 1 155.2 89211 3055.0
## <none> 89055 3056.0
## - lunch_type:transport_means 1 306.2 89362 3056.0
## - test_prep:transport_means 1 380.6 89436 3056.5
## + gender:is_first_child 1 165.2 88890 3056.9
## + parent_educ:practice_sport 10 2832.5 86223 3056.9
## + is_first_child:transport_means 1 94.7 88961 3057.3
## + lunch_type:test_prep 1 36.5 89019 3057.7
## + gender:test_prep 1 19.6 89036 3057.8
## + gender:transport_means 1 16.0 89039 3057.9
## + test_prep:wkly_study_hours 2 307.5 88748 3057.9
## + gender:lunch_type 1 5.0 89050 3057.9
## + test_prep:is_first_child 1 2.3 89053 3057.9
## + gender:wkly_study_hours 2 281.6 88774 3058.1
## + test_prep:practice_sport 2 274.1 88781 3058.2
## + parent_marital_status:transport_means 3 536.1 88519 3058.4
## + parent_educ:is_first_child 5 1120.5 87935 3058.5
## + ethnic_group:parent_marital_status 11 2866.7 86189 3058.7
## + parent_educ:parent_marital_status 15 4025.6 85030 3058.7
## + practice_sport:transport_means 2 128.4 88927 3059.1
## + ethnic_group:lunch_type 4 727.7 88328 3059.1
## + transport_means:wkly_study_hours 2 91.2 88964 3059.4
## + test_prep:parent_marital_status 3 363.7 88692 3059.6
## + is_first_child:wkly_study_hours 2 59.9 88996 3059.6
## - parent_marital_status:wkly_study_hours 6 2422.9 91478 3059.8
## - lunch_type:wkly_study_hours 2 1192.1 90248 3059.8
## + ethnic_group:test_prep 4 620.7 88435 3059.8
## + practice_sport:is_first_child 2 13.6 89042 3059.9
## + lunch_type:parent_marital_status 3 260.3 88795 3060.2
## - ethnic_group:transport_means 4 1888.2 90944 3060.3
## - lunch_type:practice_sport 2 1306.9 90362 3060.6
## + gender:ethnic_group 4 493.9 88561 3060.7
## + gender:parent_marital_status 3 188.4 88867 3060.7
## + parent_educ:wkly_study_hours 10 2257.7 86798 3060.8
## + parent_marital_status:practice_sport 6 871.7 88184 3062.2
## + ethnic_group:is_first_child 4 259.4 88796 3062.2
## + parent_educ:transport_means 5 535.3 88520 3062.4
## + ethnic_group:practice_sport 8 1361.2 87694 3062.9
## + gender:parent_educ 5 452.5 88603 3063.0
## - parent_marital_status:is_first_child 3 2116.2 91172 3063.8
## + parent_educ:lunch_type 5 311.0 88744 3063.9
## + parent_educ:test_prep 5 246.7 88809 3064.3
## + ethnic_group:wkly_study_hours 8 414.2 88641 3069.2
## + ethnic_group:parent_educ 20 2184.6 86871 3081.3
## - parent_educ 5 6212.6 95268 3085.8
##
## Step: AIC=3053.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:is_first_child 1 104.8 90075 3052.7
## - gender:practice_sport 2 480.0 90450 3053.1
## - lunch_type:transport_means 1 253.2 90223 3053.7
## <none> 89970 3054.0
## - test_prep:transport_means 1 362.9 90333 3054.4
## + gender:is_first_child 1 220.7 89749 3054.5
## + is_first_child:transport_means 1 78.8 89891 3055.5
## + lunch_type:test_prep 1 55.0 89915 3055.6
## + test_prep:wkly_study_hours 2 329.5 89640 3055.8
## + gender:test_prep 1 17.9 89952 3055.9
## + test_prep:is_first_child 1 8.8 89961 3055.9
## + gender:transport_means 1 6.2 89964 3055.9
## + practice_sport:wkly_study_hours 4 914.5 89055 3056.0
## + gender:lunch_type 1 3.0 89967 3056.0
## + test_prep:practice_sport 2 288.9 89681 3056.1
## + parent_educ:practice_sport 10 2683.0 87287 3056.1
## + gender:wkly_study_hours 2 260.5 89709 3056.3
## + parent_marital_status:transport_means 3 536.5 89433 3056.5
## - ethnic_group:transport_means 4 1731.1 91701 3057.2
## + transport_means:wkly_study_hours 2 106.2 89864 3057.3
## + practice_sport:transport_means 2 105.7 89864 3057.3
## + is_first_child:wkly_study_hours 2 105.5 89864 3057.3
## - lunch_type:wkly_study_hours 2 1121.3 91091 3057.3
## + parent_educ:parent_marital_status 15 3959.8 86010 3057.4
## + parent_educ:is_first_child 5 962.3 89008 3057.7
## + ethnic_group:parent_marital_status 11 2751.1 87219 3057.7
## + test_prep:parent_marital_status 3 339.8 89630 3057.8
## + ethnic_group:test_prep 4 625.2 89345 3057.9
## + practice_sport:is_first_child 2 16.4 89954 3057.9
## + ethnic_group:lunch_type 4 613.6 89356 3058.0
## - lunch_type:practice_sport 2 1223.0 91193 3058.0
## + gender:ethnic_group 4 541.3 89429 3058.4
## - parent_marital_status:wkly_study_hours 6 2566.6 92537 3058.6
## + gender:parent_marital_status 3 213.7 89756 3058.6
## + lunch_type:parent_marital_status 3 185.9 89784 3058.8
## + parent_educ:wkly_study_hours 10 2163.2 87807 3059.6
## + ethnic_group:is_first_child 4 308.4 89662 3060.0
## + parent_educ:transport_means 5 606.4 89364 3060.0
## + parent_marital_status:practice_sport 6 804.4 89166 3060.7
## + gender:parent_educ 5 467.2 89503 3060.9
## + ethnic_group:practice_sport 8 1351.5 88618 3061.1
## - parent_marital_status:is_first_child 3 2027.1 91997 3061.1
## + parent_educ:lunch_type 5 369.3 89601 3061.6
## + parent_educ:test_prep 5 264.7 89705 3062.3
## + ethnic_group:wkly_study_hours 8 442.1 89528 3067.1
## + ethnic_group:parent_educ 20 2078.3 87892 3080.2
## - parent_educ 5 6298.3 96268 3083.9
##
## Step: AIC=3052.68
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + lunch_type:practice_sport +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:transport_means + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:practice_sport 2 526.0 90601 3052.1
## - lunch_type:transport_means 1 243.3 90318 3052.3
## <none> 90075 3052.7
## - test_prep:transport_means 1 340.3 90415 3052.9
## + gender:is_first_child 1 202.2 89873 3053.3
## + lunch_type:is_first_child 1 104.8 89970 3054.0
## + is_first_child:transport_means 1 77.3 89997 3054.2
## + lunch_type:test_prep 1 62.2 90012 3054.3
## + gender:test_prep 1 14.6 90060 3054.6
## + test_prep:is_first_child 1 11.9 90063 3054.6
## + gender:transport_means 1 3.2 90072 3054.7
## + gender:lunch_type 1 2.1 90073 3054.7
## + test_prep:wkly_study_hours 2 305.6 89769 3054.7
## + test_prep:practice_sport 2 299.1 89776 3054.7
## + practice_sport:wkly_study_hours 4 864.0 89211 3055.0
## + gender:wkly_study_hours 2 256.1 89819 3055.0
## + parent_marital_status:transport_means 3 532.3 89542 3055.2
## + parent_educ:practice_sport 10 2607.2 87468 3055.3
## + parent_educ:parent_marital_status 15 4009.3 86065 3055.8
## + is_first_child:wkly_study_hours 2 126.1 89949 3055.8
## - ethnic_group:transport_means 4 1728.8 91804 3055.9
## + transport_means:wkly_study_hours 2 113.9 89961 3055.9
## + practice_sport:transport_means 2 112.5 89962 3055.9
## - lunch_type:wkly_study_hours 2 1152.6 91227 3056.2
## + test_prep:parent_marital_status 3 350.7 89724 3056.4
## + parent_educ:is_first_child 5 948.3 89126 3056.4
## - lunch_type:practice_sport 2 1201.6 91276 3056.5
## + practice_sport:is_first_child 2 20.0 90055 3056.6
## + ethnic_group:lunch_type 4 607.8 89467 3056.7
## + ethnic_group:test_prep 4 594.8 89480 3056.8
## + gender:ethnic_group 4 554.4 89520 3057.0
## + ethnic_group:parent_marital_status 11 2638.8 87436 3057.1
## + gender:parent_marital_status 3 203.9 89871 3057.3
## + lunch_type:parent_marital_status 3 174.4 89900 3057.5
## - parent_marital_status:wkly_study_hours 6 2636.8 92712 3057.7
## + ethnic_group:is_first_child 4 345.1 89730 3058.4
## + parent_educ:wkly_study_hours 10 2142.9 87932 3058.5
## + parent_educ:transport_means 5 600.4 89474 3058.7
## + gender:parent_educ 5 465.6 89609 3059.6
## + ethnic_group:practice_sport 8 1357.1 88718 3059.7
## + parent_marital_status:practice_sport 6 716.6 89358 3060.0
## - parent_marital_status:is_first_child 3 2113.0 92188 3060.4
## + parent_educ:lunch_type 5 343.3 89731 3060.4
## + parent_educ:test_prep 5 264.1 89811 3060.9
## + ethnic_group:wkly_study_hours 8 452.4 89622 3065.7
## + ethnic_group:parent_educ 20 2115.9 87959 3078.7
## - parent_educ 5 6269.5 96344 3082.4
##
## Step: AIC=3052.12
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:transport_means 1 262.4 90863 3051.8
## <none> 90601 3052.1
## - test_prep:transport_means 1 326.9 90928 3052.2
## + gender:practice_sport 2 526.0 90075 3052.7
## + gender:is_first_child 1 218.3 90382 3052.7
## + lunch_type:is_first_child 1 150.8 90450 3053.1
## + is_first_child:transport_means 1 90.8 90510 3053.5
## + lunch_type:test_prep 1 63.7 90537 3053.7
## + gender:test_prep 1 21.3 90579 3054.0
## + test_prep:practice_sport 2 327.6 90273 3054.0
## + practice_sport:wkly_study_hours 4 930.4 89670 3054.0
## + gender:transport_means 1 8.0 90593 3054.1
## + test_prep:is_first_child 1 7.2 90594 3054.1
## + gender:lunch_type 1 2.4 90598 3054.1
## + test_prep:wkly_study_hours 2 303.1 90298 3054.1
## + gender:wkly_study_hours 2 298.6 90302 3054.2
## + parent_marital_status:transport_means 3 501.6 90099 3054.8
## + parent_educ:parent_marital_status 15 4059.5 86541 3055.1
## + transport_means:wkly_study_hours 2 140.5 90460 3055.2
## + is_first_child:wkly_study_hours 2 130.1 90471 3055.3
## - ethnic_group:transport_means 4 1762.1 92363 3055.5
## + practice_sport:transport_means 2 85.4 90515 3055.6
## - lunch_type:wkly_study_hours 2 1156.5 91757 3055.6
## + parent_educ:is_first_child 5 955.4 89645 3055.9
## + ethnic_group:parent_marital_status 11 2757.1 87844 3055.9
## + test_prep:parent_marital_status 3 340.6 90260 3055.9
## + practice_sport:is_first_child 2 14.2 90587 3056.0
## - lunch_type:practice_sport 2 1234.5 91835 3056.1
## + ethnic_group:test_prep 4 608.3 89992 3056.1
## + parent_educ:practice_sport 10 2370.5 88230 3056.5
## + ethnic_group:lunch_type 4 550.1 90051 3056.5
## - parent_marital_status:wkly_study_hours 6 2560.9 93162 3056.6
## + gender:ethnic_group 4 526.6 90074 3056.7
## + gender:parent_marital_status 3 213.9 90387 3056.7
## + lunch_type:parent_marital_status 3 164.7 90436 3057.0
## + ethnic_group:is_first_child 4 357.4 90243 3057.8
## + parent_educ:transport_means 5 589.9 90011 3058.3
## + ethnic_group:practice_sport 8 1489.7 89111 3058.3
## + parent_educ:wkly_study_hours 10 2057.4 88543 3058.6
## + gender:parent_educ 5 482.3 90118 3059.0
## - parent_marital_status:is_first_child 3 2053.4 92654 3059.3
## + parent_marital_status:practice_sport 6 723.2 89878 3059.4
## + parent_educ:lunch_type 5 389.3 90212 3059.6
## + parent_educ:test_prep 5 259.3 90341 3060.4
## + ethnic_group:wkly_study_hours 8 436.2 90165 3065.3
## + ethnic_group:parent_educ 20 2189.7 88411 3077.7
## - parent_educ 5 6278.7 96879 3081.7
## - gender 1 8889.6 99490 3105.3
##
## Step: AIC=3051.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## test_prep:transport_means + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:transport_means 1 300.1 91163 3051.8
## <none> 90863 3051.8
## + lunch_type:transport_means 1 262.4 90601 3052.1
## + gender:is_first_child 1 254.3 90609 3052.2
## + gender:practice_sport 2 545.1 90318 3052.3
## + lunch_type:is_first_child 1 138.9 90724 3052.9
## + is_first_child:transport_means 1 89.3 90774 3053.2
## + lunch_type:test_prep 1 40.2 90823 3053.6
## + gender:test_prep 1 27.3 90836 3053.6
## + test_prep:is_first_child 1 16.5 90847 3053.7
## + gender:transport_means 1 13.3 90850 3053.7
## + test_prep:practice_sport 2 311.6 90551 3053.8
## + gender:lunch_type 1 0.7 90862 3053.8
## + gender:wkly_study_hours 2 303.7 90559 3053.8
## + practice_sport:wkly_study_hours 4 876.1 89987 3054.1
## + test_prep:wkly_study_hours 2 231.4 90632 3054.3
## + parent_marital_status:transport_means 3 501.6 90362 3054.6
## + parent_educ:parent_marital_status 15 4074.5 86789 3054.8
## + transport_means:wkly_study_hours 2 135.8 90727 3054.9
## + is_first_child:wkly_study_hours 2 130.2 90733 3055.0
## - ethnic_group:transport_means 4 1751.0 92614 3055.1
## - lunch_type:wkly_study_hours 2 1125.4 91989 3055.1
## + practice_sport:transport_means 2 93.8 90769 3055.2
## - lunch_type:practice_sport 2 1176.8 92040 3055.4
## + test_prep:parent_marital_status 3 352.3 90511 3055.5
## + ethnic_group:parent_marital_status 11 2754.8 88108 3055.7
## + practice_sport:is_first_child 2 18.0 90845 3055.7
## + parent_educ:is_first_child 5 919.1 89944 3055.8
## + ethnic_group:test_prep 4 595.6 90267 3055.9
## + ethnic_group:lunch_type 4 591.5 90272 3056.0
## + gender:parent_marital_status 3 236.6 90627 3056.3
## - parent_marital_status:wkly_study_hours 6 2586.1 93449 3056.4
## + parent_educ:practice_sport 10 2339.6 88524 3056.4
## + gender:ethnic_group 4 509.1 90354 3056.5
## + lunch_type:parent_marital_status 3 183.6 90680 3056.6
## + ethnic_group:is_first_child 4 324.0 90539 3057.7
## + parent_educ:transport_means 5 598.1 90265 3057.9
## + gender:parent_educ 5 547.4 90316 3058.3
## + parent_educ:wkly_study_hours 10 2035.7 88827 3058.4
## + ethnic_group:practice_sport 8 1397.2 89466 3058.7
## + parent_marital_status:practice_sport 6 746.8 90116 3058.9
## - parent_marital_status:is_first_child 3 2062.9 92926 3059.1
## + parent_educ:lunch_type 5 398.6 90465 3059.2
## + parent_educ:test_prep 5 285.8 90577 3060.0
## + ethnic_group:wkly_study_hours 8 399.8 90463 3065.2
## + ethnic_group:parent_educ 20 2151.2 88712 3077.7
## - parent_educ 5 6148.1 97011 3080.4
## - gender 1 8826.3 99689 3104.5
##
## Step: AIC=3051.77
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## <none> 91163 3051.8
## + test_prep:transport_means 1 300.1 90863 3051.8
## + gender:is_first_child 1 257.6 90906 3052.1
## + lunch_type:transport_means 1 235.6 90928 3052.2
## + gender:practice_sport 2 530.8 90632 3052.3
## + lunch_type:is_first_child 1 114.5 91049 3053.0
## + is_first_child:transport_means 1 108.6 91055 3053.1
## + lunch_type:test_prep 1 42.2 91121 3053.5
## + gender:transport_means 1 24.2 91139 3053.6
## + gender:test_prep 1 23.3 91140 3053.6
## + test_prep:is_first_child 1 18.2 91145 3053.7
## + test_prep:practice_sport 2 325.8 90837 3053.7
## + gender:wkly_study_hours 2 322.6 90841 3053.7
## + gender:lunch_type 1 0.0 91163 3053.8
## + practice_sport:wkly_study_hours 4 872.4 90291 3054.1
## + parent_educ:parent_marital_status 15 4174.7 86989 3054.1
## - lunch_type:wkly_study_hours 2 997.2 92160 3054.2
## + parent_marital_status:transport_means 3 537.0 90626 3054.3
## + test_prep:wkly_study_hours 2 211.0 90952 3054.4
## + is_first_child:wkly_study_hours 2 140.3 91023 3054.9
## + transport_means:wkly_study_hours 2 101.6 91062 3055.1
## + practice_sport:transport_means 2 92.2 91071 3055.2
## + test_prep:parent_marital_status 3 391.9 90771 3055.2
## - lunch_type:practice_sport 2 1208.9 92372 3055.5
## + parent_educ:is_first_child 5 948.5 90215 3055.6
## + ethnic_group:parent_marital_status 11 2759.5 88404 3055.6
## + practice_sport:is_first_child 2 16.4 91147 3055.7
## + ethnic_group:lunch_type 4 617.0 90546 3055.8
## - ethnic_group:transport_means 4 1874.3 93037 3055.8
## - parent_marital_status:wkly_study_hours 6 2516.2 93679 3055.8
## + ethnic_group:test_prep 4 578.0 90585 3056.0
## + gender:parent_marital_status 3 248.6 90915 3056.2
## + parent_educ:practice_sport 10 2364.5 88799 3056.3
## + gender:ethnic_group 4 528.5 90635 3056.3
## + lunch_type:parent_marital_status 3 187.1 90976 3056.6
## + ethnic_group:is_first_child 4 297.7 90866 3057.8
## + parent_educ:transport_means 5 601.1 90562 3057.9
## + gender:parent_educ 5 541.0 90622 3058.3
## + ethnic_group:practice_sport 8 1451.3 89712 3058.3
## + parent_educ:wkly_study_hours 10 2050.0 89113 3058.3
## + parent_marital_status:practice_sport 6 769.8 90393 3058.8
## + parent_educ:lunch_type 5 420.7 90743 3059.0
## - parent_marital_status:is_first_child 3 2087.3 93251 3059.1
## + parent_educ:test_prep 5 312.8 90850 3059.7
## + ethnic_group:wkly_study_hours 8 406.7 90757 3065.1
## + ethnic_group:parent_educ 20 2088.9 89074 3078.1
## - test_prep 1 4865.5 96029 3080.4
## - parent_educ 5 6366.3 97530 3081.6
## - gender 1 8627.7 99791 3103.1
summary(stepwise_model_read)
##
## Call:
## lm(formula = reading_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours,
## data = df_4_mdl_read)
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.540 -8.273 -0.267 9.481 33.728
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 64.0126 5.6402 11.349
## gendermale -7.9731 1.1041 -7.221
## ethnic_groupgroup B 4.0052 3.7361 1.072
## ethnic_groupgroup C 4.5817 3.4195 1.340
## ethnic_groupgroup D 4.6170 3.5000 1.319
## ethnic_groupgroup E 13.9574 3.8663 3.610
## parent_educbachelor's degree 3.3736 1.9408 1.738
## parent_educhigh school -5.9247 1.6817 -3.523
## parent_educmaster's degree 3.4397 2.4234 1.419
## parent_educsome college -2.3224 1.6870 -1.377
## parent_educsome high school -5.3232 1.6969 -3.137
## lunch_typestandard 2.0599 3.8020 0.542
## test_prepnone -6.2162 1.1463 -5.423
## parent_marital_statusmarried 10.2557 4.0650 2.523
## parent_marital_statussingle -0.8882 4.4420 -0.200
## parent_marital_statuswidowed 17.2457 10.8292 1.593
## practice_sportregularly -4.4245 3.2294 -1.370
## practice_sportsometimes -5.4217 3.1279 -1.733
## is_first_childyes 8.8087 3.3685 2.615
## transport_meansschool_bus 7.1540 3.8499 1.858
## wkly_study_hours> 10 -15.1280 5.0552 -2.993
## wkly_study_hours10-May 1.2358 3.6575 0.338
## ethnic_groupgroup B:transport_meansschool_bus -8.5078 4.6456 -1.831
## ethnic_groupgroup C:transport_meansschool_bus -8.7787 4.3480 -2.019
## ethnic_groupgroup D:transport_meansschool_bus -2.4914 4.4269 -0.563
## ethnic_groupgroup E:transport_meansschool_bus -12.1513 4.8881 -2.486
## lunch_typestandard:practice_sportregularly 4.3134 3.9100 1.103
## lunch_typestandard:practice_sportsometimes 9.0693 3.8110 2.380
## lunch_typestandard:wkly_study_hours> 10 6.1827 3.4568 1.789
## lunch_typestandard:wkly_study_hours10-May -1.3341 2.6912 -0.496
## parent_marital_statusmarried:is_first_childyes -10.3012 3.6911 -2.791
## parent_marital_statussingle:is_first_childyes -2.7153 4.1037 -0.662
## parent_marital_statuswidowed:is_first_childyes -11.5351 8.6888 -1.328
## parent_marital_statusmarried:wkly_study_hours> 10 11.8333 4.9161 2.407
## parent_marital_statussingle:wkly_study_hours> 10 20.4572 5.5006 3.719
## parent_marital_statuswidowed:wkly_study_hours> 10 5.7848 14.3577 0.403
## parent_marital_statusmarried:wkly_study_hours10-May 1.7018 3.6640 0.464
## parent_marital_statussingle:wkly_study_hours10-May 5.0455 4.1368 1.220
## parent_marital_statuswidowed:wkly_study_hours10-May -3.6043 10.7836 -0.334
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## gendermale 1.72e-12 ***
## ethnic_groupgroup B 0.284174
## ethnic_groupgroup C 0.180841
## ethnic_groupgroup D 0.187673
## ethnic_groupgroup E 0.000334 ***
## parent_educbachelor's degree 0.082717 .
## parent_educhigh school 0.000462 ***
## parent_educmaster's degree 0.156352
## parent_educsome college 0.169188
## parent_educsome high school 0.001798 **
## lunch_typestandard 0.588175
## test_prepnone 8.79e-08 ***
## parent_marital_statusmarried 0.011918 *
## parent_marital_statussingle 0.841585
## parent_marital_statuswidowed 0.111840
## practice_sportregularly 0.171222
## practice_sportsometimes 0.083598 .
## is_first_childyes 0.009167 **
## transport_meansschool_bus 0.063672 .
## wkly_study_hours> 10 0.002890 **
## wkly_study_hours10-May 0.735589
## ethnic_groupgroup B:transport_meansschool_bus 0.067585 .
## ethnic_groupgroup C:transport_meansschool_bus 0.043967 *
## ethnic_groupgroup D:transport_meansschool_bus 0.573809
## ethnic_groupgroup E:transport_meansschool_bus 0.013218 *
## lunch_typestandard:practice_sportregularly 0.270437
## lunch_typestandard:practice_sportsometimes 0.017661 *
## lunch_typestandard:wkly_study_hours> 10 0.074233 .
## lunch_typestandard:wkly_study_hours10-May 0.620296
## parent_marital_statusmarried:is_first_childyes 0.005440 **
## parent_marital_statussingle:is_first_childyes 0.508448
## parent_marital_statuswidowed:is_first_childyes 0.184867
## parent_marital_statusmarried:wkly_study_hours> 10 0.016410 *
## parent_marital_statussingle:wkly_study_hours> 10 0.000220 ***
## parent_marital_statuswidowed:wkly_study_hours> 10 0.687173
## parent_marital_statusmarried:wkly_study_hours10-May 0.642503
## parent_marital_statussingle:wkly_study_hours10-May 0.223116
## parent_marital_statuswidowed:wkly_study_hours10-May 0.738324
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.86 on 551 degrees of freedom
## Multiple R-squared: 0.3254, Adjusted R-squared: 0.2789
## F-statistic: 6.995 on 38 and 551 DF, p-value: < 2.2e-16
